<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



<TABLE>
<S>                                           <C>
For the Quarter Ended
    March 31, 1999                            Commission File Number  0-18650 
---------------------                         --------------------------------
</TABLE>


                   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, 1999 


<TABLE>
<S>                                                                        <C>
PART I - FINANCIAL INFORMATION

Item 1.

  Index to Financial Statements

    Balance Sheets

      March 31, 1999 (unaudited)                                             3

      December 31, 1998                                                      4

    Statements of Revenue and Expenses (unaudited)

      For the three months ended March 31, 1999                              5

      For the three months ended March 31, 1998                              6

    Statements of Changes in Partners' Equity

      For the three months ended March 31, 1999
         (unaudited)                                                         7

    Statements of Cash Flows (unaudited)

      For the three months ended March 31, 1999                              8

      For the three months ended March 31, 1998                              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
</TABLE>


                                       2
<PAGE>   3
                   DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
                                 BALANCE SHEETS
                                 March 31, 1999
                                  (Unaudited)


<TABLE>
<CAPTION>
                                     Liquidating    Continuing               
                                       Limited       Limited                 
                                      Partners       Partners       Total    
                                    ------------   ------------  ----------- 
<S>                                <C>             <C>         <C>          
ASSETS                                                                      

Cash and cash equivalents            $ 2,413,017   $ 7,163,953   $ 9,576,970
Net investment in direct financing
  leases                                    --         234,891       234,891
Residual interest in CRCA                   --            --            --
Diverted and other assets, net           176,327       616,511       792,838
Datronic assets, net                        --            --            --
                                     -----------   -----------   -----------

                                     $ 2,589,344   $ 8,015,355   $10,604,699
                                     ===========   ===========   ===========

LIABILITIES AND PARTNERS' EQUITY

Accounts payable and accrued
  expenses                           $    14,391   $    57,026   $    71,417
Lessee rental deposits                     7,277        41,044        48,321
                                     -----------   -----------   -----------

    Total liabilities                     21,668        98,070       119,738

Total partners' equity                 2,567,676     7,917,285    10,484,961
                                     -----------   -----------   -----------

                                     $ 2,589,344   $ 8,015,355   $10,604,699
                                     ===========   ===========   ===========
</TABLE>


                 See accompanying notes to financial statements

                                       3
<PAGE>   4
                   DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
                                 BALANCE SHEETS
                               December 31, 1998


<TABLE>
<CAPTION>
                                     Liquidating    Continuing               
                                       Limited       Limited                 
                                      Partners       Partners       Total    
                                    ------------   ------------  ----------- 
<S>                                <C>             <C>          <C>          
ASSETS

Cash and cash equivalents            $ 2,417,775   $ 7,094,146   $ 9,511,921
Judgment receivable, net                  29,673       103,747       133,420
Net investment in direct financing
  leases                                    --         314,607       314,607
Residual interest in CRCA                   --            --            --
Diverted and other assets, net           176,327       616,511       792,838
Datronic assets, net                        --            --            --
                                     -----------   -----------   -----------

                                     $ 2,623,775   $ 8,129,011   $10,752,786
                                     ===========   ===========   ===========

LIABILITIES AND PARTNERS' EQUITY

Accounts payable and accrued
  expenses                           $    17,395   $    71,160   $    88,555
Lessee rental deposits                     9,434        53,240        62,674
                                     -----------   -----------   -----------

    Total liabilities                     26,829       124,400       151,229

Total partners' equity                 2,596,946     8,004,611    10,601,557
                                     -----------   -----------   -----------

                                     $ 2,623,775   $ 8,129,011   $10,752,786
                                     ===========   ===========   ===========
</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, 1999
                                  (Unaudited)


<TABLE>
<CAPTION>
                                   Liquidating  Continuing 
                                     Limited     Limited 
                                    Partners     Partners       Total
                                  ------------  -----------  -----------
<S>                                <C>          <C>         <C>
Revenue:
  Lease income                       $   1,944    $  19,666    $  21,610
  Interest income                       21,595       84,151      105,746
                                     ---------    ---------    ---------

                                        23,539      103,817      127,356
                                     ---------    ---------    ---------

Expenses:
  General Partner's expense
    reimbursement                       44,665      172,431      217,096
  Professional fees                     10,492       41,587       52,079
  Other operating expenses               1,005        3,850        4,855
  Credit for lease losses               (3,353)     (26,725)     (30,078)
                                     ---------    ---------    ---------

                                        52,809      191,143      243,952
                                     ---------    ---------    ---------

Net loss                             $ (29,270)   $ (87,326)   $(116,596)
                                     =========    =========    =========

Net loss - General Partner           $    (293)   $    (873)   $  (1,166)
                                     =========    =========    =========

Net loss - Limited Partners          $ (28,977)   $ (86,453)   $(115,430)
                                     =========    =========    =========

Net loss per limited
   partnership unit                  $   (0.65)   $   (0.56)
                                     =========    =========

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, 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

                                       6

<PAGE>   7
                   DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
                   STATEMENTS 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, 1998 *   $       --      $  2,596,946    $  8,004,611    $ 10,601,557

  Net loss                           (1,166)        (28,977)        (86,453)       (116,596)
  Allocation of General
    Partner's Equity                  1,166            (293)           (873)           --
                               ------------    ------------    ------------    ------------

Balance, March 31, 1999        $       --      $  2,567,676    $  7,917,285    $ 10,484,961
                               ============    ============    ============    ============
</TABLE>


*  Balances are net of $56,896 and $296,111 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, 1999
                                  (Unaudited)

<TABLE>
<CAPTION>
                                         Liquidating    Continuing               
                                           Limited       Limited                 
                                          Partners       Partners         Total    
                                        ------------    -----------    -----------
<S>                                      <C>            <C>           <C>
Cash flows from operating activities:
  Net loss                               $   (29,270)   $   (87,326)   $  (116,596)
  Adjustments to reconcile net loss
     to net cash used in operating
    activities:
    Credit for lease losses                   (3,353)       (26,725)       (30,078)
    Changes in assets and liabilities:
      Judgment receivable, net                29,673        103,747        133,420
      Accounts payable and
        accrued expenses                      (3,004)       (14,134)       (17,138)
      Lessee rental deposits                  (2,157)       (12,196)       (14,353)
                                         -----------    -----------    -----------
                                              (8,111)       (36,634)       (44,745)
                                         -----------    -----------    -----------

Cash flows from investing activities:
  Principal collections on leases              3,353        106,441        109,794
                                         -----------    -----------    -----------

Net increase (decrease) in cash and
  cash equivalents                            (4,758)        69,807         65,049
Cash and cash equivalents:
  Beginning of year                        2,417,775      7,094,146      9,511,921
                                         -----------    -----------    -----------
  End of first quarter                   $ 2,413,017    $ 7,163,953    $ 9,576,970
                                         ===========    ===========    ===========
</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, 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

                                       9
<PAGE>   10

                   DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
                         NOTES TO FINANCIAL STATEMENTS
                                 March 31, 1999
                                  (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 1998 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 1998 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 1998 Form 10-K.

NOTE 3 - LIMITED PARTNERSHIP DISTRIBUTIONS:

In early April 1999, the Partnership made a cash distribution to Limited
Partners who were owners of record on December 31, 1998. This distribution
consisted of two components: (i) the net proceeds from the Price Waterhouse and
Weiss & Company legal actions ($127,000 and $446,000 for Liquidating and
Continuing Limited Partners respectively), and (ii) residual cash resulting
from the net cash flows of the Partnership ($1,629,000 and $4,173,000 for
Liquidating and Continuing Limited Partners respectively). The portion of the
distribution attributable to legal action proceeds was allocated to each
Limited Partner based on the number of units held at the rate of $2.87 per
unit. See Note 8 to the Partnership's financial statements included in the 1998
Form 10-K. Pursuant to the Partnership Agreement, residual cash was allocated 
to each Limited Partner based on their proportionate share of total partners'
capital attributable to their Class.

NOTE 4 - RESIDUAL INTEREST IN CRCA:

Residual interest in CRCA represents the Partnership's fully reserved 65% (35%
for Fund XX) interest in the remaining assets of Computer Rental Corp. of
America, Inc. (CRCA). These assets consisted of a $4.2 million subordinated
note receivable from Personal Computer Rental Corporation (PCR) and $136,000 of
cash. See Note 4 to the


                                      10
<PAGE>   11

                   DATRONIC EQUIPMENT INCOME FUND XVIII, L.P.
                 NOTES TO THE FINANCIAL STATEMENTS - CONTINUED


financial statements included in the 1998 Form 10-K. In early April, 1999, CRCA
sold the $4.2 million subordinated note to PCR's senior secured creditor for
$250,000. The Partnership's share of these proceeds along with its share of
CRCA's residual cash, after payment of expenses, will be credited to its
provision for lease losses when distributed to the Partnership.


                                      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,
1998 through March 31, 1999. The discussion and analysis of results of
operations is for the three month period ended March 31, 1999 as compared to
the corresponding period in 1998. Any capitalized term not defined herein has 
been defined or discussed in the Partnership's 1998 Form 10-K.

Liquidity and Capital Resources

During the three months ended March 31, 1999, Partnership assets continued to
be converted to cash in order to pay Partnership operating expenses and provide
for the ultimate liquidation of the Partnership. During the three months ended
March 31, 1999, Partnership cash and cash equivalents increased by $65,000 to
$9,577,000 at March 31, 1999 from $9,512,000 at December 31, 1998. This
increase is primarily due to cash receipts from collections on leases of
$110,000, partially offset by cash used in operations of $45,000.

In early April 1999, the Partnership made a cash distribution to Limited
Partners who were owners of record on December 31, 1998. This distribution
consisted of two components: (i) the net proceeds from the Price Waterhouse and
Weiss & Company legal actions ($127,000 and $446,000 for Liquidating and
Continuing Limited Partners respectively), and (ii) residual cash resulting
from the net cash flows of the Partnership ($1,629,000 and $4,173,000 for
Liquidating and Continuing Limited Partners respectively). The portion of the
distribution attributable to legal action proceeds was allocated to each
Limited Partner based on the number of units held at the rate of $2.87 per
unit. See Note 8 to the Partnership's financial statements included in the 1998
Form 10-K. Pursuant to the Partnership Agreement, residual cash was allocated 
to each Limited Partner based on their proportionate share of total partners'
capital attributable to their Class.

The Partnership's sources of future liquidity are expected to come from
remaining cash-on-hand after the April 1999 distribution, the cash receipts
from leases owned by the Partnership as well as the disposition of Diverted
Assets (consisting primarily of an office building in Schaumburg, Illinois).
The lease portfolio is scheduled to be fully liquidated by May 2000. The
general partner expects the Diverted Assets to be converted to cash during 1999
thereby enabling the Partnership to pay an additional distribution in early
2000. After all assets are disposed of and the proceeds are distributed to the
limited partners, the Partnership will be required to file final


                                      12
<PAGE>   13

reports with the Securities and Exchange Commission and the Internal Revenue
Service. The general partner expects this to occur sometime during the year
2000.

Results of Operations

The Partnership had a net loss of $117,000 for the three months ended March 31,
1999 in the aggregate for all classes of partners. This compares to net
earnings of $173,000 for the three months ended March 31, 1998. Differences in
operating results between Liquidating and Continuing Limited Partners are
attributable to lease income 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 periods ended March 31, 1999 and 1998 include
the following:

Lease income:

Since April 1995, the Partnership has been in its Liquidating 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. This trend will continue as the Partnership liquidates its
remaining leases.

Interest income:

Interest income includes earnings on invested cash balances. Interest income
for 1999 was higher than 1998 because of higher average invested cash balances.

General Partner's expense reimbursement:

General Partner's expense reimbursement includes payments to LRC for expenses
it incurred as general partner in excess of those covered by its partner
distributions. These expenses include expenses incurred by LRC in its
management of the day-to-day operations of the Partnership.

Professional fees:

Professional fees for the three months ended March 31, 1999 reflect a
decreasing level of professional services required as a result of the decrease
in the Partnership's lease portfolio and related activities. Included in the
1998 amount are fees paid in connection with the litigation against the
Partnership's former accountants.

Credit for lease losses:

This credit reflects recovery of previously reserved balances. The 1998 amount
also includes a $384,000 recovery against the Master Lease agreement with CRCA.
See Note 4 to the Partnership's financial statements included in the 1998 Form
10-K.

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

The information called for in this disclosure is not applicable to the 
Registrant.


                                      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, 1998 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 10th day of May 1999.





            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.



<PAGE>   16

                          INDEX TO EXHIBITS 


<TABLE>
<CAPTION>
EXHIBIT 
NUMBER                        DESCRIPTION
-------                       -----------
  <S>               <C>
   27               Financial Data Schedule, which is submitted electronically
                    to the Securities and Exchange Commission for information
                    only and not filed.
</TABLE>