<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D. C. 20549
                                    FORM 10-Q


(Mark One)


[X]         Quarterly report pursuant to Section 13 or 15(d) of the
                        Securities Exchange Act of 1934

                 For the quarterly period ended June 30, 1998 or

[ ]         Transition report pursuant to Section 13 or 15(d) of the
                        Securities Exchange Act of 1934

         For the transition period from                    to
                                        ------------------   ------------------

                         Commission File Number       1-7908
                                                ------------------

                         ADAMS RESOURCES & ENERGY, INC.
             (Exact name of Registrant as specified in its charter)


           Delaware                                        74-1753147
 (State or other jurisdiction of                       (I.R.S. Employer
 incorporation or organization)                       Identification No.)


                      5 Post Oak Park, Houston, Texas 77027
               (Address of principal executive office & Zip Code)


       Registrant's telephone number, including area code    (713)  881-3600
                                                           ------------------

     Indicate by check mark whether the Registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

                                 Yes   X    No
                                    ------     ------

The number of shares of Common Stock of the Registrant, par value $.10 per
share, outstanding at July 31, 1998 was 4,217,596.
                      -------------     ---------


<PAGE>   2



                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                 UNAUDITED CONSOLIDATED STATEMENT OF OPERATIONS
                      (IN THOUSANDS, EXCEPT PER SHARE DATA)


<TABLE>
<CAPTION>
                                                     Six Months Ended          Three Months Ended
                                                         June 30,                   June 30,
                                                 -----------------------     -----------------------
                                                   1998           1997         1998          1997
                                                 ---------     ---------     ---------     ---------
<S>                                              <C>           <C>           <C>           <C>      
REVENUE:
  Marketing                                      $ 860,706     $ 917,467     $ 454,329     $ 432,855
  Transportation                                    16,992        14,271         8,329         7,581
  Oil & Gas                                          3,516         4,422         1,920         1,579
                                                 ---------     ---------     ---------     ---------
                                                   881,214       936,160       464,578       442,015
                                                 ---------     ---------     ---------     ---------

COSTS AND EXPENSES:
Operating
   Marketing                                       856,572       916,434       452,099       432,887
   Transportation                                   14,890        11,446         7,356         6,153
   Oil & Gas                                         1,939           794         1,637           359
Corporate general and administrative                 1,157         1,077           614           541
Depreciation, depletion and amortization             4,252         2,752         2,059         1,139
                                                 ---------     ---------     ---------     ---------
                                                   878,810       932,503       463,765       441,079
                                                 ---------     ---------     ---------     ---------
Operating earnings                                   2,404         3,657           813           936


OTHER INCOME (EXPENSE):
Property sales and other                               108           615          --             261
Interest                                              (146)         (128)          (81)          (41)
                                                 ---------     ---------     ---------     ---------
                                                       (38)          487           (81)          220
                                                 ---------     ---------     ---------     ---------

Earnings before income taxes                         2,366         4,144           732         1,156
Income tax provision
   Current                                             702           171           208            40
   Deferred                                            200         1,375           100           400
                                                 ---------     ---------     ---------     ---------
                                                       902         1,546           308           440
                                                 ---------     ---------     ---------     ---------

NET EARNINGS                                     $   1,464     $   2,598     $     424     $     716
                                                 =========     =========     =========     =========

PER COMMON SHARE DATA:
   Basic and diluted net earnings                $     .35     $     .62     $     .10     $     .17
                                                 =========     =========     =========     =========

   Dividends                                     $    --       $    --       $    --       $    --
                                                 =========     =========     =========     =========
</TABLE>





   The accompanying notes are an integral part of these financial statements.

                                      - 2 -
<PAGE>   3

                MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                       CONDITION AND RESULTS OF OPERATIONS


Results of Operations

               Six Months Comparison

               - Marketing

               Marketing division revenues and operating earnings were as
     follows (in thousands):

<TABLE>
<CAPTION>
                                               Six Months Ended         Three Months Ended
                                                   June 30,                   June 30,
                                            ----------------------    ----------------------
                                              1998         1997          1998        1997
                                            ---------    ---------    ---------    ---------

<S>                                         <C>          <C>          <C>          <C>      
          Revenues                          $ 860,706    $ 917,467    $ 454,329    $ 432,855

          Operating earnings (loss)         $   2,577    $     540    $   1,452    $    (282)
</TABLE>

               Gross revenues for the Company's Marketing operations were
     reduced by $56,761,000 or 6%, in the comparative current period as a result
     of reduced average crude oil prices partially offset by greater volumes of
     crude oil purchased at the wellhead. Compared to last year's first half,
     average crude oil sales prices were reduced by approximately 38% in 1998 as
     crude oil fell to the $13 per barrel range. Average wellhead purchases were
     105,000 barrels per day in 1998 versus 60,000 barrels per day in 1997.
     Marketing division operating margins for the first six months of 1998
     increased to $2,577,000 because of the reversal of the unusually
     unfavorable market conditions that existed in 1997.


               - Transportation

               Transportation revenues and operating earnings were as follows
     (in thousands):

<TABLE>
<CAPTION>
                                        Six Months Ended      Three Months Ended
                                            June 30,              June 30,
                                       ------------------    ------------------
                                        1998       1997       1998       1997
                                       -------    -------    -------    -------

<S>                                    <C>        <C>        <C>        <C>    
          Revenues                     $16,992    $14,271    $ 8,329    $ 7,581

          Operating earnings           $ 1,659    $ 2,518    $   740    $ 1,266
</TABLE>


               Transportation revenues increased in 1998 because recent
     equipment additions enabled the Company to handle a larger volume of
     business. Operating earnings were reduced, however, when


                                     - 3 -
<PAGE>   4

     sales volumes did not grow as fast as anticipated due to an apparent 
     general slowing of the United States economy. As noted, in order to service
     a larger volume of business, the Company expanded capacity which
     necessitated increased fixed costs. When the rate of sales volume growth
     slowed, the new higher level of fixed cost caused the earnings decline.


               - Oil and Gas

               Oil and gas division revenues and operating earnings were as
     follows (in thousands):

<TABLE>
<CAPTION>
                                             Six Months Ended     Three Months Ended
                                                  June 30,              June 30,
                                            -------------------    -------------------
                                             1998        1997       1998        1997
                                            -------     -------    -------     -------

<S>                                         <C>         <C>        <C>         <C>    
          Revenues                          $ 3,516     $ 4,422    $ 1,920     $ 1,579

          Operating earnings (loss)         $  (675)    $ 1,676    $  (765)    $   493
</TABLE>

               Oil and gas revenues decreased for the comparative six month
     period as a result of reduced crude oil and natural gas prices. For the
     comparative current quarter revenues were improved primarily as a result of
     increased crude oil sales volumes. Volumes and prices compare as follows:

<TABLE>
<CAPTION>
                                                     Six Months Ended                          Three Months Ended
                                             ----------------------------------       -------------------------------------
                                                1998                  1997                 1998                  1997
                                                ----                  ----                 ----                  ----
<S>                                          <C>                   <C>                 <C>                  <C>             
     Crude oil
        Volume                               36,200 Bbls.          31,500 Bbls.         19,200 Bbls.            11,300 Bbls.
        Average price                        $13.75/ Bbl           $21.14/ Bbl.        $ 13.03/ Bbl.        $    19.28/ Bbl.

     Natural gas
        Volume                             1,625,000 Mcf         1,700,000 Mcf          825,000 Mcf             810,000 Mcf
        Average price                         $1.95/ Mcf            $2.24/ Mcf           $1.99/ Mcf         $     1.78/ Mcf
</TABLE>

               Oil and gas operating earnings decreased in 1998 in part because
     of the reduced pricing scenario. In addition, during the second quarter of
     1998, the Company incurred and expensed $1,044,000 of 3D seismic
     geophysical costs. The Company continues to participate in the seismic
     study and expects to incur and expense approximately $320,000 of additional
     3D seismic costs during the third quarter of 1998. The Company currently
     anticipates participating in the drilling of the first test well on the
     prospective acreage during the fourth quarter of 1998.


               - Other

               The provision for depreciation, depletion and amortization is
     increased in 1998 because of a larger capitalized cost base. Recently
     included in the depreciable cost base is the Company's offshore Louisiana
     crude oil pipeline completed at a cost of $4.2 million and placed in
     service in


                                     - 4 -
<PAGE>   5

     January 1998. Property sales and other income for 1998 resulted
     primarily from the sale of a former gasoline service station location while
     1997 included a $401,000 recovery from an insurance carrier for prior year
     overcharges and a $215,000 gain realized on the sale of twenty-one truck
     tractors.

         - Three Months Comparisons

         Comparisons for the three month period ended June 30, 1998 are
consistent with the discussions provided above.


     Liquidity and Capital Resources

               During the first six months of 1998, the Company invested
     $4,462,000 in property additions with $1,256,000 going towards oil and gas
     drilling efforts and the remainder for various marketing and transportation
     equipment items. Funding for these investments was derived from the Company
     generating $5,479,000 of working capital funds. The $1,193,000 of excess
     cash flow was applied to general working capital needs.

               During the second quarter of 1998, the Company's primary lending
     bank increased the Company's borrowing availability under its oil and gas
     working capital line to $5 million. As of June 30, 1998, total available
     working capital borrowing capacity was $9.2 million with $6.7 million
     outstanding. Refer to the "Liquidity and Capital Resources" section of the
     Company's Annual Report on Form 10-K for the year ended December 31, 1997
     for additional discussion of the Company's bank relationships, tax
     carryforwards and other matters.







                                     - 5 -
<PAGE>   6


                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                           June 30,    December 31,
                                                                             1998          1997
                                                                           ---------     ---------
                                                                          (Unaudited)
<S>                                                                        <C>           <C>      
          ASSETS

          Current assets:
            Cash and cash equivalents .................................    $   3,250     $   6,496
            Accounts receivable, net ..................................       51,606        73,806
            Inventories ...............................................        6,047         5,092
            Prepaid and other .........................................        1,188         1,675
                                                                           ---------     ---------
                          Total current assets ........................       62,091        87,069
                                                                           ---------     ---------

          Property and equipment ......................................       60,588        56,298
            Less - accumulated depreciation,
                   depletion and amortization .........................      (34,475)      (30,361)
                                                                           ---------     ---------
                                                                              26,113        25,937
                                                                           ---------     ---------


          Other assets ................................................        1,342         1,277
                                                                           ---------     ---------
                                                                           $  89,546     $ 114,283
                                                                           =========     =========


          LIABILITIES AND SHAREHOLDERS' EQUITY

          Current liabilities:
            Accounts payable ..........................................    $  49,486     $  74,829
            Accrued and other liabilities .............................        2,963         3,475
            Current maturities of long-term debt ......................           36            71
                                                                           ---------     ---------
                   Total current liabilities ..........................       52,485        78,375

          Long-term debt, less current maturities .....................        6,700         6,900
          Other liabilities ...........................................          759           870
                                                                           ---------     ---------
                                                                              59,944        86,145

          Shareholders' equity:
            Preferred stock - $1.00 par value, 960,000 shares
                authorized, none outstanding ..........................         --            --
            Common stock - $.10 par value, 7,500,000
                shares authorized, 4,217,596 shares
                outstanding, respectively .............................          422           422
            Contributed capital .......................................       11,693        11,693
            Retained earnings since December 31, 1992 .................       17,487        16,023
                                                                           ---------     ---------
                   Total shareholders' equity .........................       29,602        28,138
                                                                           ---------     ---------
                                                                           $  89,546     $ 114,283
                                                                           =========     =========
</TABLE>


   The accompanying notes are an integral part of these financial statements.




                                     - 6 -
<PAGE>   7


                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                 UNAUDITED CONSOLIDATED STATEMENT OF CASH FLOWS
                                 (IN THOUSANDS)


<TABLE>
<CAPTION>
                                                                                 Six Months Ended
                                                                                     June 30,
                                                                               ---------------------
                                                                                 1998        1997
                                                                               --------     --------

<S>                                                                            <C>          <C>     
CASH PROVIDED (USED) BY OPERATIONS:
            Net earnings ..................................................    $  1,464     $  2,598
            Items of income not requiring (providing) cash -
              Depreciation, depletion and amortization ....................       4,252        2,752
              Deferred income tax provision ...............................        --            725
              Gain on sale of properties ..................................         (61)        (215)
              Other, net ..................................................        (176)        (218)
            Decrease (increase) in accounts receivable ....................      22,200       16,716
            Decrease (increase) in inventories ............................        (955)         761
            Decrease (increase) in prepaid and other ......................         487          198
            Increase (decrease) in accounts payable .......................     (25,343)     (15,574)
            Increase (decrease) in accrued liabilities ....................        (512)        (709)
                                                                               --------     --------

              Net cash provided (required) by operating activities ........       1,356        7,034
                                                                               --------     --------

          INVESTING ACTIVITIES:
            Property and equipment additions ..............................      (4,462)      (4,156)
            Proceeds from property sales ..................................          95          425
                                                                               --------     --------

              Net cash provided by (used in) investing activities .........      (4,367)      (3,731)
                                                                               --------     --------

          FINANCING ACTIVITIES:
            Repayment of debt .............................................        (235)      (3,331)
            Sales of stock ................................................        --             43
                                                                               --------     --------

              Net cash provided by (used in) financing activities .........        (235)      (3,288)
                                                                               --------     --------

          Increase (decrease) in cash and cash equivalents ................      (3,246)          15

          Cash at beginning of period .....................................       6,496        3,782
                                                                               --------     --------

          Cash at end of period ...........................................    $  3,250     $  3,797
                                                                               ========     ========

          Supplemental disclosure of cash flow information:

            Interest paid during the period ...............................    $    146     $     87
                                                                               ========     --------

            Income taxes paid during the period ...........................    $    513     $    867
                                                                               ========     ========
</TABLE>




   The accompanying notes are an integral part of these financial statements.



                                     - 7 -
<PAGE>   8




                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES
                               NOTES TO UNAUDITED
                        CONSOLIDATED FINANCIAL STATEMENTS


Note 1 - Basis of Presentation

         The accompanying condensed financial statements are unaudited but, in
the opinion of the Company's management, include all adjustments (consisting of
normal recurring accruals) necessary for a fair presentation of financial
position at June 30, 1998 and December 31, 1997 and results of operations and
cash flows for the six months ended June 30, 1998 and 1997. Certain information
and note disclosures normally included in annual financial statements prepared
in accordance with generally accepted accounting principles have been condensed
or omitted pursuant to Securities and Exchange Commission rules and regulations,
although the Company believes the disclosures made are adequate to make the
information presented not misleading. It is suggested these condensed financial
statements be read in conjunction with the financial statements, and the notes
thereto, included in the Company's latest annual report on Form 10-K. The
interim statement of operations is not necessarily indicative of results to be
expected for a full year.

         When used in this document, the words "anticipate", "believe",
"expect", "estimate", "project", and similar expressions are intended to
identify forward-looking statements. Such statements are subject to certain
risks, uncertainties and assumptions. Should one or more of these risks or
uncertainties materialize, or should underlying assumptions prove incorrect,
actual results may vary materially from those anticipated, believed, expected or
projected.

         In February 1997, the Financial Accounting Standards Board ("FASB")
issued Statement of Financial Accounting Standards ("SFAS") No. 128, "Earnings
Per Share", which established new standards for computing and presenting
earnings per share. The provisions of the statement are effective for fiscal
years ending after December 15, 1997, and accordingly, have been adopted in the
accompanying financial statements. Under the provisions of SFAS No. 128, the
presentation of primary earnings per share has been replaced with basic earnings
per share, and fully diluted earnings per share presentations have been replaced
with diluted earnings per share for potentially dilutive securities. Prior
period earnings per share data have been restated. Earnings per share are based
on the weighted average number of shares of common stock and common stock
equivalents outstanding during the period. Such shares outstanding averaged
4,217,596 shares for 1998 and 4,213,596 shares for 1997.

Note 2 - New Accounting Standards

         In June 1997, the FASB issued SFAS No. 130, "Reporting Comprehensive
Income", which establishes standards for reporting and display of comprehensive
income and its components in a full set of general-purpose financial statements.
The statement requires (a)

                                     - 8 -
<PAGE>   9

                 ADAMS RESOURCES & ENERGY, INC. AND SUBSIDIARIES

classification of items of other comprehensive income by their nature in a
financial statement and (b) display of the accumulated balance of other
comprehensive income separate from retained earnings and additional paid-in
capital in the equity section of a statement of financial position. SFAS No. 130
is effective for interim periods beginning after December 15, 1997. For the six
month period and for the quarters ended June 30, 1998, and 1997, there are no
differences between the Company's "traditional" and "comprehensive" net income.

         In June 1997, the FASB also issued SFAS No. 131, "Disclosure about
Segments of an Enterprise and Related Information", which establishes standards
for reporting information about operating segments in annual financial
statements and requires that selected information be reported about the
operating segments in interim financial reports issued to the shareholders. It
also establishes standards for related disclosure about products and services,
geographic areas, and major customers. The Company has concluded that its
segment information as currently reported is in compliance with SFAS No. 131 and
as such, adoption has no effect on current or prior period presentations.

         In June 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities". The Statement establishes accounting and
reporting standards requiring that every derivative instrument (including
certain derivative instruments embedded in other contracts) be recorded in the
balance sheet as either an asset or liability measured at its fair value. The
Statement requires that changes in the derivatives fair value be recognized
currently in earnings unless specific hedge accounting criteria are met. Special
accounting for qualifying hedges allows a derivative's gains and losses to
offset related results on the hedged item in the income statement, and requires
that a company must formally document, designate, and assess the effectiveness
of transactions that receive hedge accounting. SFAS 133 is required to be
effective for fiscal years beginning after June 15, 1999 and may be adopted
early. The Company has not yet quantified the impact (if any) of adopting SFAS
133.

                           PART II. OTHER INFORMATION
Item 1. - None

Item 2. - None

Item 3. - None

Item 4. - None

Item 6.  Exhibits and Reports on Form 8-K
   a.   Exhibits - None.
   b.   Reports on Form 8-K - None.



                                     - 9 -
<PAGE>   10


         Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                        ADAMS RESOURCES & ENERGY, INC.
                                        (Registrant)



Date:    August 12, 1998

                                        By  /s/ K. S. Adams, Jr.
                                            ------------------------------------
                                            K. S. Adams, Jr.
                                            Chief Executive Officer



                                        By  /s/ Richard B. Abshire
                                            ------------------------------------
                                            Richard B. Abshire
                                            Chief Financial Officer




                                     - 10 -
<PAGE>   11


                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
Exhibit
Number             Description
-------            -----------

<S>     <C>        <C>
27*      -         Financial Data Schedule
</TABLE>

----------
*  - Filed herewith