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


(Mark One)

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

                For the quarterly period ended March 31, 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 May 12, 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>

                                                                                            Three Months Ended
                                                                                                March 31,
                                                                                        --------------------------
                                                                                            1998           1997
                                                                                        -----------    -----------
Revenues:
<S>                                                                                     <C>            <C>        
  Marketing.......................................................                      $   406,377    $   484,612
  Transportation..................................................                            8,663          6,690
  Oil and Gas.....................................................                            1,596          2,843
                                                                                        -----------    -----------
                                                                                            416,636        494,145

Costs and expenses:
  Operating
   Marketing......................................................                          404,473        483,547
   Transportation.................................................                            7,534          5,293
   Oil and gas....................................................                              302            435
  Corporate general and administrative............................                              543            536
  Depreciation, depletion and amortization........................                            2,193          1,613
                                                                                        -----------    -----------
                                                                                            415,045        491,424

Operating earnings................................................                            1,591          2,721

Other income (expense)............................................
  Property sales and other........................................                              108            354
  Interest........................................................                              (65)           (87)
                                                                                        -----------    -----------

Earnings before income taxes......................................                            1,634          2,988
Income tax provision
  Current.........................................................                              494            131
  Deferred........................................................                              100            975
                                                                                        -----------    -----------
                                                                                                594          1,106
                                                                                        -----------    -----------

Net earnings......................................................                      $     1,040    $     1,882
                                                                                        ===========    ===========

Basic and diluted net earnings                                                          $       .25    $       .45
                                                                                        ===========    ===========
  per common share................................................

Dividends per common share........................................                      $        --    $        --
                                                                                        ===========    ===========
</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


     Three Months Comparison


     -  Marketing

     Gross revenues for the Company's Marketing operations decreased by
$78,235,000 or 16%, in the comparative current period as a result of reduced
average crude oil prices partially offset by increased volumes of crude oil
purchased at the wellhead. Compared to last year's first quarter, average crude
oil sales prices were decreased by approximately 40% in 1998. In contrast,
average wellhead purchases of crude oil were 105,000 barrels per day in 1998
versus 60,000 barrels per day in 1997. Marketing division operating margins
before depreciation for the first three months of 1998 increased to $1,904,000
versus $1,065,000 in the similar 1997 period. Marketing operating earnings
increased as a result of the increased volumes purchased at the wellhead.


     - Transportation

     Transportation revenues and operating earnings before depreciation
increased (decreased) as follows:
<TABLE>
<CAPTION>

                                                                                                          Percentage
                                                               First Quarter           First Quarter       Increase
                                                                   1998                    1997           (Decrease)
                                                              ---------------        ----------------     ----------

              <S>                                             <C>                     <C>                 <C>
              Revenues                                         $  8,663,000            $    6,690,000         29%
              Operating earnings
                  before depreciation                          $  1,129,000            $    1,397,000        (19)%
</TABLE>


     The Transportation division revenue increase during 1998 resulted from
continued growth in customer demand coupled with expanded capacity (in terms of
trucks and drivers) to manage such demand. On a comparative basis, operating
earnings suffered in the current quarter because it was necessary to expand
capacity in anticipation of increased customer demand. Thus fixed costs grew
faster than demand for the Company's services. As customer demand continues to
grow, profitability will be enhanced.


     - Oil and Gas

     Oil and gas revenues and operating earnings decreased for the comparative
current first 

                                     - 3 -
<PAGE>   4

quarter as a result of reduced comparative crude oil and natural gas prices and
volumes. Volumes and prices compare as follows:
<TABLE>
<CAPTION>

                                                                       First Quarter             First Quarter
                                                                             1998                      1997
                                                                       -------------             ---------------
              Crude oil
              <S>                                                      <C>                       <C>
                      Volume                                           17,000 Bbls.                  20,000 Bbls.
                      Average price                                    $  14.56/Bbl.              $   22.16/Bbl.

              Natural gas
                      Volume                                            800,000 Mcf                 900,000 Mcf
                      Average price, includes value
                       of associated gas liquids                       $   1.70 Mcf               $    2.73 Mcf
</TABLE>

     The Company has entered into a "Geophysical Exploration Agreement" that
affords the Company an 8% interest in a 30 month seismic option covering 93,000
net acres in Willacy County, Texas. An approximate 200 square mile 3-D seismic
program will commence in May 1998. The Company's net share of such seismic costs
(approximately $1.2 million) will be expensed in the second and third quarters
of 1998 as incurred.

     - Other income (expense)

     The provision for depreciation, depletion and amortization ("DD&A") is
increased in the current quarter with increased capital costs associated with
the Company's significant level of property additions during 1997 and 1998.
Included in such capitalized costs is approximately $4 million incurred to
construct an offshore crude oil pipeline. The pipeline costs are being amortized
over a period of approximately five years. Included in first quarter 1998 DD&A
is approximately $300.000 of pipeline amortization.

     Property sales and other income of $108,000 and $354,000, respectively,
resulted from gains realized on the sale of a former gasoline service station
location during 1998, and from the sale of twenty-one truck tractors in 1997.
Interest expense is reduced in 1998 because the Company used its excess cash
flow to reduce its level of long term debt.

Liquidity and Capital Resources

     During the first three months of 1998, the Company invested $2,040,000 in
property and equipment additions with $798,000 used for 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
$3,142,000 of working capital funds. The $1,102,000 of excess cash flow
generated was applied against the Company's working capital lines of credit.

     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 and other matters.


                                     - 4 -
<PAGE>   5


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

<TABLE>
<CAPTION>

                                                                           March 31,            December 31,
                                                                             1998                   1997
                                                                         ------------          --------------
                                                                         (Unaudited)
<S>                                                                      <C>                   <C>
ASSETS

Current assets:
  Cash and cash equivalents...................................           $      4,939          $      6,496
  Accounts receivable, net....................................                 61,256                73,806
  Inventories.................................................                  1,536                 5,092
  Prepaid and other...........................................                  1,088                 1,675
                                                                          -----------          ------------

                Total current assets..........................                 68,819                87,069
                                                                         ------------          ------------

Property and equipment........................................                 58,084                56,298
  Less - accumulated depreciation,
         depletion and amortization...........................                (32,323)              (30,361)
                                                                         ------------          ------------
                                                                               25,761                25,937
                                                                         ------------          ------------


Other assets..................................................                  1,251                  1,277
                                                                         ------------          -------------
                                                                         $     95,831          $     114,283
                                                                         ============          =============


LIABILITIES AND SHAREHOLDERS' EQUITY

Current liabilities:
  Accounts payable............................................           $     58,339          $      74,829
  Accrued and other liabilities...............................                  2,966                  3,475
  Current maturities of long-term debt........................                     36                     71
                                                                         ------------          -------------
         Total current liabilities............................                 61,341                 78,375

Long-term debt, less current maturities.......................                  4,500                  6,900
Other liabilities.............................................                    812                    870
                                                                         ------------          -------------
                                                                               66,653                 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.............................................                    422                    422
  Contributed capital.........................................                 11,693                 11,693
  Retained earnings since December 31, 1992...................                 17,063                 16,023
                                                                         ------------          -------------
         Total shareholders' equity ..........................                 29,178                 28,138
                                                                         ------------          -------------
                                                                         $     95,831          $     114,283
                                                                         ============          =============
</TABLE>


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



                                     - 5 -
<PAGE>   6


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

                                                                                              Three Months Ended
                                                                                                 March 31,
                                                                                        ---------------------------
                                                                                           1998             1997
                                                                                        ----------       ----------
<S>                                                                                     <C>              <C>
CASH PROVIDED (USED) BY OPERATIONS:
  Net earnings ..................................................................       $    1,040       $    1,882
  Items of income not requiring (providing) cash -
    Depreciation, depletion and amortization ....................................            2,193            1,613
    Deferred income tax provision ...............................................               --              975
    Gain on sale of properties...................................................              (59)            (354)
    Other, net ..................................................................              (32)             (48)
  Decrease (increase) in accounts receivable ....................................           12,550           10,608
  Decrease (increase) in inventories ............................................            3,556              284
  Decrease (increase) in prepaid and other ......................................              587              211
  Increase (decrease) in accounts payable .......................................          (16,490)          (9,857)
  Increase (decrease) in accrued liabilities ....................................             (509)          (1,090)
                                                                                        -----------      ----------

    Net cash provided (required) by operating activities ........................            2,836            4,224
                                                                                        ----------       ----------

INVESTING ACTIVITIES:
  Property and equipment additions ..............................................           (2,040)          (1,001)
  Proceeds from property sales ..................................................               82              425
                                                                                        ----------       ----------

    Net cash provided by (used in) investing activities .........................           (1,958)            (576)
                                                                                        ----------       ----------

FINANCING ACTIVITIES:
  Repayment of debt .............................................................           (2,435)          (3,181)
  Sales of stock ................................................................               --               43
                                                                                        ----------       ----------

    Net cash provided by (used in) financing activities .........................           (2,435)          (3,138)
                                                                                        ----------       ----------

Increase (decrease) in cash and cash equivalents.................................           (1,557)              510

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

Cash at end of period............................................................       $    4,939       $    4,292
                                                                                        ==========       ==========

Supplemental disclosure of cash flow information:

  Interest paid during the period ...............................................       $       65       $       87
                                                                                        ==========       ==========

  Income taxes paid during the period............................................       $       --       $       10
                                                                                        ==========       ==========
</TABLE>



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

                                     - 6 -

<PAGE>   7


                 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 March 31, 1998 and December 31, 1997 and results of operations and
cash flows for the three months ended March 31, 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.

         In February 1997, the Financial Accounting Standards Board ("FASB")
issued 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) 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 quarters ended March 31, 1998, and 1997, there is no
differences between the Company's "traditional" and "comprehensive" net income.


                                     - 7 -
<PAGE>   8

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

         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.


                           PART II. OTHER INFORMATION

Item 1. - None

Item 2. - None

Item 3. - None

Item 4. - Submission of Matters to a Vote of Security Holders

         The 1998 Annual Meeting of Stockholders (the "Meeting") of the Company
was held on April 29, 1998. At the Meeting, holders of common stock, $.10 par
value, of the Company ("Common Stock"), elected nine members of the Company's
Board of Directors.

         Out of the 4,217,596 shares of Common Stock entitled to vote at the
Meeting, there were 3,916,318 shares of Common Stock voted for the election of
the nominees for Directors listed in the proxy statement.

Item 6.  Exhibits and Reports on Form 8K

     a.   Exhibits - None.
     b.   Reports on Form 8-K - None.



                                     - 8 -
<PAGE>   9


     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:    May 13, 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



                                     - 9 -
<PAGE>   10

                                  EXHIBIT INDEX


<TABLE>
<CAPTION>
Exhibit
Number             Description
------             -----------
<S>                <C>         
27*      -         Financial Data Schedule
</TABLE>

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