This is an enormously complicated task, and probably can't be done efficiently
in Excel, if at all. The only solution that might work is Solver, where you
put a 0 in the column next to the receipt amounts, then tell Solver to change
the 0's to 1's until the SUMIF for the rows with a 1 is equal to the deposit
amount. But you say an "enormous list", and I expect Solver will tell you that
it can't find a solution.
If you need to know this, you really should mark each receipt with the deposit
date from the outset.