<PAGE>   1


                                UNITED STATES
                     SECURITIES AND EXCHANGE COMMISSION
                           Washington, D.C. 20549
                                  Form 10-Q
                      Quarterly Report Under Section 13
                         or 15 (d) of the Securities
                            Exchange Act of 1934
                      ---------------------------------


For the Quarter Ended
    March 31, 1998                           Commission File Number  0-18650
---------------------                        -------------------------------


                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
                 ------------------------------------------
           (Exact name of Registrant as specified in its charter)


    Delaware                                               36-3639399
----------------                                 ---------------------------
State or other                                   IRS Employer Identification
jurisdiction of                                  Number
incorporation or
organization

1300 E. Woodfield Road, Suite 312                Schaumburg, Illinois 60173
---------------------------------                --------------------------
 Address of principal                               City, State, Zip Code
 executive offices

Registrant's telephone number:                          (847) 240-6200
                                                 --------------------------



     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.



                    (1)  Yes  x   No
                             ---    ---
                    (2)  Yes  x   No
                             ---    ---




<PAGE>   2



                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                                  FORM 10-Q

                    FOR THE QUARTER ENDED MARCH 31, 1998

                       PART I - FINANCIAL INFORMATION


Item 1.


 Index to Financial Statements

   Balance Sheets

     March 31, 1998 (unaudited)                                             3

     December 31, 1997                                                      4

   Statements of Revenue and Expenses (unaudited)

     For the three months ended March 31, 1998                              5

     For the three months ended March 31, 1997                              6

   Statements of Changes in Partners' Equity

     For the three months ended March 31, 1998                              7
         (unaudited)

   Statements of Cash Flows (unaudited)

     For the three months ended March 31, 1998                              8

     For the three months ended March 31, 1997                              9

   Notes to Financial Statements (unaudited)                          10 - 11

Item 2.


  Management's Discussion and Analysis of
    Financial Condition and Results of Operations                     12 - 13


                         PART II - OTHER INFORMATION

Items 1-6.                                                                 14


                                      2



<PAGE>   3




                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                               BALANCE SHEETS

                               March 31, 1998
                                 (Unaudited)

                                      
<TABLE>
<CAPTION>
                                       Liquidating  Continuing
                                         Limited     Limited
                                        Partners     Partners      Total
                                       -----------  ----------  -----------
     <S>                               <C>          <C>         <C>
     ASSETS
     ------
     Cash and cash equivalents          $2,269,109  $6,004,317  $ 8,273,426
     Net investment in direct
       financing leases                          -     849,247      849,247
     Residual interest in CRCA                   -           -            -
     Diverted and other assets, net        340,788   1,191,530    1,532,318
     Datronic assets, net                        -           -            -
                                        ----------  ----------  -----------

                                        $2,609,897  $8,045,094  $10,654,991
                                        ==========  ==========  ===========


     LIABILITIES AND PARTNERS' EQUITY
     --------------------------------

     Accounts payable and
       accrued expenses                 $   14,741  $   61,497  $    76,238
     Lessee rental deposits                 17,513      90,250      107,763
                                        ----------  ----------  -----------

       Total liabilities                    32,254     151,747      184,001

     Total partners' equity              2,577,643   7,893,347   10,470,990
                                        ----------  ----------  -----------

                                        $2,609,897  $8,045,094  $10,654,991
                                        ==========  ==========  ===========
</TABLE>


               See accompanying notes to financial statements.


                                      
                                      3

                                      

<PAGE>   4



                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                               BALANCE SHEETS

                              December 31, 1997


<TABLE>
<CAPTION>
                                       Liquidating  Continuing
                                         Limited     Limited
                                        Partners     Partners      Total
                                       -----------  ----------  -----------
     <S>                               <C>          <C>         <C>
     ASSETS
     ------
     Cash and cash equivalents          $2,253,955  $5,662,905  $ 7,916,860
     Net investment in direct
       financing leases                          -   1,045,601    1,045,601
     Residual interest in CRCA                   -           -            -
     Diverted and other assets, net        340,788   1,191,530    1,532,318
     Datronic assets, net                        -           -            -
                                        ----------  ----------  -----------

                                        $2,594,743  $7,900,036  $10,494,779
                                        ==========  ==========  ===========


     LIABILITIES AND PARTNERS' EQUITY
     --------------------------------

     Accounts payable and
       accrued expenses                 $   15,101  $   68,413  $    83,514
     Lessee rental deposits                 18,786      94,702      113,488
                                        ----------  ----------  -----------

       Total liabilities                    33,887     163,115      197,002

     Total partners' equity              2,560,856   7,736,921   10,297,777
                                        ----------  ----------  -----------

                                        $2,594,743  $7,900,036  $10,494,779
                                        ==========  ==========  ===========
</TABLE>


               See accompanying notes to financial statements.

                                      

                                      4



<PAGE>   5


                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                     STATEMENTS OF REVENUE AND EXPENSES

                  For the three months ended March 31, 1998

                                 (Unaudited)

<TABLE>
<CAPTION>
                                       Liquidating  Continuing
                                         Limited     Limited
                                        Partners     Partners     Total
                                       -----------  ----------  ---------
      <S>                              <C>          <C>         <C>
      Revenue:
       Lease income                    $     7,460  $   60,628  $  68,088
       Interest income                      21,691      81,548    103,239
                                       -----------  ----------  ---------

                                            29,151     142,176    171,327
                                       -----------  ----------  ---------

      Expenses:
       General Partner's
        expense reimbursement               48,263     189,248    237,511
       Professional fees                    53,639     189,054    242,693
       Other operating expenses              3,147      11,512     14,659
       Credit for lease losses             (92,685)   (404,064)  (496,749)
                                       -----------  ----------  ---------

                                            12,364     (14,250)    (1,886)
                                       -----------  ----------  ---------


      Net earnings                     $    16,787  $  156,426  $ 173,213
                                       ===========  ==========  =========


      Net earnings - General Partner   $       168  $    1,564  $   1,732
                                       ===========  ==========  =========


      Net earnings - Limited Partners  $    16,619  $  154,862  $ 171,481
                                       ===========  ==========  =========

      Net earnings per limited
       partnership unit                     $ 0.37     $  1.00
                                            ======     =======
                                                       
      Weighted average number                          
       of limited partnership units                    
       outstanding                          44,468     155,509
                                            ======     =======
</TABLE>


               See accompanying notes to financial statements.



                                      5

                                      

<PAGE>   6



                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                     STATEMENTS OF REVENUE AND EXPENSES

                  For the three months ended March 31, 1997
                                 (Unaudited)

<TABLE>
<CAPTION>
                                      Liquidating  Continuing
                                        Limited     Limited
                                       Partners     Partners     Total
                                      -----------  ----------  ---------
       <S>                            <C>          <C>         <C>
       Revenue:
        Lease income                  $     3,426  $  105,741  $ 109,167
        Interest income                    13,710      61,193     74,903
                                      -----------  ----------  ---------

                                           17,136     166,934    184,070
                                      -----------  ----------  ---------

       Expenses:
        General Partner's
         expense reimbursement             99,432     357,110    456,542
        Professional fees                  16,284      60,652     76,936
        Other operating expenses            4,366      16,125     20,491
        Credit for lease losses          (100,642)   (246,886)  (347,528)
                                      -----------  ----------  ---------

                                           19,440     187,001    206,441
                                      -----------  ----------  ---------


       Net loss                       $    (2,304) $  (20,067) $ (22,371)
                                      ===========  ==========  =========


       Net loss - General Partner     $       (23) $     (201) $    (224)
                                      ===========  ==========  =========


       Net loss - Limited Partners    $    (2,281) $  (19,866) $ (22,147)
                                      ===========  ==========  =========

       Net loss per limited
        partnership unit                   $ (.05)    $  (.13)
                                           ======     =======
                                                      
       Weighted average number                        
        of limited partnership units                  
        outstanding                        44,468     155,509
                                           ======     =======
</TABLE>


               See accompanying notes to financial statements.



                                      6



<PAGE>   7



                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                  STATEMENT OF CHANGES IN PARTNERS' EQUITY
                                 (Unaudited)


<TABLE>
<CAPTION>
                                          Liquidating  Continuing
                                General     Limited     Limited       Total
                               Partner's   Partners'   Partners'    Partners'
                                Equity      Equity       Equity      Equity
                               ---------  -----------  ----------  -----------
  <S>                          <C>        <C>          <C>         <C>


  Balance, December 31, 1997*  $       -   $2,560,856  $7,736,921  $10,297,777

   Net earnings                    1,732       16,619     154,862      173,213
   Allocation of General
    Partner's Equity              (1,732)         168       1,564            -
                               ---------  -----------  ----------  -----------

  Balance, March 31, 1998      $       -   $2,577,643  $7,893,347  $10,470,990
                               =========  ===========  ==========  ===========
</TABLE>

*    Balances are net of $57,257 and $298,788, of General Partner's equity
     previously allocated to Liquidating and Continuing Limited Partners'
     Equity.


               See accompanying notes to financial statements.



                                      7

                                      
<PAGE>   8



                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
                          STATEMENTS OF CASH FLOWS
                  For the three months ended March 31, 1998
                                 (Unaudited)

<TABLE>
<CAPTION>
                                    Liquidating  Continuing
                                      Limited     Limited
                                     Partners     Partners     Total
                                    -----------  ----------  ----------
        <S>                         <C>          <C>         <C>
        Cash flows from operating
         activities:
         Net earnings               $    16,787  $  156,426  $  173,213
         Adjustments to reconcile
          net earnings to net cash
          used in operating
          activities:
          Credit for lease losses       (92,685)   (404,064)   (496,749)
          Changes in assets and
           liabilities:
           Accounts payable and
            accrued expenses               (360)     (6,916)     (7,276)
           Lessee rental deposits        (1,273)     (4,452)     (5,725)
                                    -----------  ----------  ----------

                                        (77,531)   (259,006)   (336,537)
                                    -----------  ----------  ----------

        Cash flows from investing
         activities:
         Principal collections
          on leases                      92,685     600,418     693,103
                                    -----------  ----------  ----------


        Net increase in cash
         and cash equivalents            15,154     341,412     356,566

        Cash and cash equivalents:
         Beginning of year            2,253,955   5,662,905   7,916,860
                                    -----------  ----------  ----------

         End of first quarter       $ 2,269,109  $6,004,317  $8,273,426
                                    ===========  ==========  ==========
</TABLE>


               See accompanying notes to financial statements.



                                      8



<PAGE>   9



                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                          STATEMENTS OF CASH FLOWS

                  For the three months ended March 31, 1997
                                 (Unaudited)

<TABLE>
<CAPTION>
                                        Liquidating  Continuing
                                          Limited     Limited
                                         Partners     Partners     Total
                                        -----------  ----------  ----------
    <S>                                 <C>          <C>         <C>
    Cash flows from operating
     activities:
     Net loss                           $    (2,304) $  (20,067) $  (22,371)
     Adjustments to reconcile net loss
      to net cash used in operating
      activities:
      Credit for lease losses              (100,642)   (246,886)   (347,528)
      Changes in assets and
       liabilities:
       Accounts payable and
        accrued expenses                    (41,901)   (161,155)   (203,056)
       Lessee rental deposits                (3,604)    (15,873)    (19,477)
       Due to management
        company                              12,674      47,002      59,676
                                        -----------  ----------  ----------

                                           (135,777)   (396,979)   (532,756)
                                        -----------  ----------  ----------

    Cash flows from investing
     activities:
     Principal collections on leases        102,294     857,044     959,338
                                        -----------  ----------  ----------

    Net increase (decrease) in cash
     and cash equivalents                   (33,483)    460,065     426,582

    Cash and cash equivalents:
     Beginning of year                    2,357,430   3,986,042   6,343,472
                                        -----------  ----------  ----------

     End of first quarter               $ 2,323,947  $4,446,107  $6,770,054
                                        ===========  ==========  ==========
</TABLE>


               See accompanying notes to financial statements.



                                      9



<PAGE>   10


                 DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.

                        NOTES TO FINANCIAL STATEMENTS

                               March 31, 1998
                                 (Unaudited)

                                      
NOTE 1 - ORGANIZATION:

Datronic Equipment Income Fund XVIII, L.P., a Delaware Limited Partnership (the
"Partnership"), was formed on April 12, 1989 for the purpose of acquiring and
leasing both high- and low-technology equipment.  See Notes 5, 8, and 10 to the
Partnership's financial statements included in the 1997 Form 10-K for a
discussion of the alleged diversion of Partnership assets in 1991 and 1992 and
the subsequent litigation and settlement, change in general partner, new
classes of limited partners established and amendments to the Partnership
Agreement that occurred.

NOTE 2 - BASIS OF FINANCIAL STATEMENTS:

The accompanying financial statements should be read in conjunction with the
Partnership's financial statements included in the 1997 Form 10-K.  The
financial information furnished herein is unaudited but in the opinion of
Management includes all adjustments necessary (all of which are normal
recurring adjustments) for a fair presentation of financial condition and
results of operations. See Note 2 to the Partnership's financial statements
included in the 1997 Form 10-K.

NOTE 3 - LIMITED PARTNERSHIP DISTRIBUTIONS:

Distributions to Liquidating Limited Partners were suspended after payment of
the July 1, 1995 distribution.  Distributions to the Continuing Limited
Partners were suspended after payment of the April 1, 1996 distribution.

NOTE 4 - SUBSEQUENT EVENT: SETTLEMENT OF LITIGATION:

On May 5, 1998, Lease Resolution Corporation (LRC), on behalf of Datronic
Equipment Income Funds XVI, XVII, XVIII, XIX, XX and Datronic Finance Income
Fund I, reached an agreement to settle all claims of the aforementioned
partnerships against Weiss & Co. ("Settlement Agreement").  (See Note 8 to the
financial statements included in the Partnership's 1997 Form 10-K).  The
Settlement Agreement is contingent upon subsequent approval by the United
States District Court dismissing Weiss & Co. as a party defendant.  Pursuant to
the terms of the Settlement Agreement, Weiss & Co. has agreed to pay LRC, on
behalf of the aforementioned partnerships, $2.4 million. LRC will determine how
these proceeds, net of contingent attorneys fees of $600,000, will be
distributed among the partnerships upon completion of the trial currently in
process with Price Waterhouse.


                                     10



<PAGE>   11



The Settlement Agreement provides for Weiss & Co. to transfer $2.4 million to   
an escrow account.  This amount will be transferred to LRC no later than 30
days following the United States District Court entering an order of dismissal
of Weiss & Co. for which no date has yet been set.  All limited partners will
be notified of the date once it has been scheduled.


                                     11



<PAGE>   12



PART I

ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS

The following discussion and analysis of liquidity and capital resources covers
material changes in the Partnership's financial condition from December 31,
1997 through March 31, 1998.  The discussion and analysis of results of
operations is for the three month period ended March 31, 1998 as compared to
the corresponding period in 1997.

Liquidity and Capital Resources

During the three months ended March 31, 1998, Partnership assets continued to
be converted to cash in order to pay Partnership operating expenses, liquidate
Partnership liabilities and increase cash balances for the ultimate liquidation
of the Partnership.

During the three months ended March 31, 1998, the Partnership's cash and cash
equivalents increased by $356,000 to $8,273,000 at March 31, 1998 from
$7,917,000 at December 31, 1997.  This increase is primarily due to cash
receipts from collections on leases of $310,000 and recovery of a portion of
the Partnership's residual interest in CRCA of $383,000, partially offset by
cash used in operations of $337,000.

The Partnership's sources of liquidity on both a long-term and short-term basis
are expected to come principally from cash-on-hand and cash receipts from
leases owned by the Partnership.  The lease portfolio is scheduled to be
substantially run out by the end of 1999, unless it is determined that it is in
the Partnership's best interest to dispose of the remaining portfolio earlier
through a bulk sale.  In addition, the Partnership's sources of liquidity on a
long-term basis include proceeds from the sale of Diverted and other assets.
Management believes that its sources of liquidity in the short and long-term
are sufficient to meet its operating cash requirements, provide for ongoing
pursuit of litigation, and an orderly liquidation of the Partnership.

The continued operation and eventual liquidation of the Partnership involves
numerous complex issues which have to be resolved.  These issues relate to the
timing and realizability of lease-related assets, Diverted and other assets,
Datronic assets, litigation and the liquidation of the other Datronic
Partnerships.  These issues make it difficult to predict the time and costs
necessary to operate and liquidate the Partnership in an orderly manner.  As a
result of these uncertainties, it is unlikely that any additional distributions
will be made until all remaining assets are liquidated and the pending
litigation is resolved.  The amount of future distributions, if any, to the
Limited Partners, in all likelihood, will be significantly less than the amount
of partners' equity reflected in the March 31, 1998 balance sheets (see
Partnership's financial statements included in Item 1).


                                     12



<PAGE>   13



Results of Operations

The Partnership had net income of $173,000 for the three months ended March 31,
1998 in the aggregate for all classes of partners.  This compares to an
aggregate net loss for the same period in 1997 of $22,000.  Differences in
operating results between Liquidating and Continuing Limited Partners are
attributable to lease income, acquisition costs, and expenses associated with
new lease investments made since the March 4, 1993 Settlement.  Liquidating
Limited Partners do not participate in these post Settlement activities.
Significant factors affecting overall operating results for the two periods
ended March 31, 1998 and 1997 include the following:

Lease income:
Since April 1995, the Partnership has been in its Liquidation Phase which
prohibits investing in any new leases.  Accordingly, the lease portfolio has
continued to decrease as collections are made, resulting in a continued decline
in lease income for the three months ended March 31, 1998 as compared to the
corresponding period in 1997.

Interest income:
Interest income increased for the three months ended March 31, 1998 as compared
to the corresponding period in 1997 as a result of increased invested cash
balances.

General Partner's expense reimbursement:
The decrease in first quarter 1998 expense is primarily due to D&O insurance
and reductions in staff and related costs.  Through the first quarter 1997,
insurance premiums were paid on an annual basis; however, in September 1997 a
one-time premium was paid that extended coverage through the ultimate
liquidation date of the Partnership.

Professional fees:
The 1998 increase reflects fees paid in connection with the ongoing litigation
against the Partnership's former accountants which is presently scheduled for
trial in May of 1998.  This increase is partially offset by the decreasing
level of professional services required in such areas as collections,
consulting and auditing.  These decreases are the result of the decrease in the
Partnership's lease portfolio and related activities.

Credit for lease losses:
This credit reflects Management's ongoing assessment of the potential losses
inherent in the lease portfolio.  The credits for 1998 and 1997 reflect
recoveries of lease balances previously reserved.  1998 and 1997 amounts also
include $384,000 and $232,000, respectively, of recoveries on the residual
interest in CRCA.  See Note 4 to the Partnership's financial statements
included in the 1997 Form 10-K.


                                     13


<PAGE>   14



PART II - OTHER INFORMATION


ITEM 1.  LEGAL PROCEEDINGS

Reference is made to Item 3 - Legal Proceedings in the Partnership's December
31, 1997 Form 10-K, for a discussion of material legal proceedings involving
the Partnership.

ITEM 2.  CHANGES IN SECURITIES

None.

ITEM 3.  DEFAULTS UPON SENIOR SECURITIES

None.

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

None.

ITEM 5.  OTHER INFORMATION

None.

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

(a)  Exhibits

See Exhibit Index.

(b)  Reports on Form 8-K

None.




                                     14



<PAGE>   15



                                 SIGNATURES


                                      
Pursuant to the requirements of the Securities Act of 1934, the Registrant has
duly caused this report to be signed on its behalf by the undersigned thereunto
duly authorized, on the 15th day of May 1998.





               DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
               Registrant




          By: /s/DONALD D. TORISKY
             ---------------------------------------
             Donald D. Torisky
             Chairman and Chief Executive Officer,
             Lease Resolution Corporation
             General Partner of
             Datronic Equipment Income Fund XVIII, L.P.



          By: /s/ROBERT P. SCHAEN
             ---------------------------------------
             Robert P. Schaen
             Vice-Chairman and Chief Financial Officer,
             Lease Resolution Corporation
             General Partner of
             Datronic Equipment Income Fund XVIII, L.P.



                                     15


<PAGE>   16



                                EXHIBIT INDEX


EXHIBIT NO.                                  DESCRIPTION
-----------                                  -----------
   27                                        Financial Data Schedule, which is
                                             submitted electronically to the
                                             Securities and Exchange Commission
                                             for information only and not filed.



                                     16