Calculate which parts make up the total sum

This sounds like the subset sum problem.  There are two ways to solve this problem in Excel: solver or create a Lambda.  Last I checked Solver is limited to about 200 variables (For our example, 1 unique number = 1 variable).

With Lambda, the approach I've used is with a bitmask to produce all possible combinations.  I avoid using DEC2BIN because of the function's limitations (In this example, it would only be good for 511 combinations.  In my demo using only 12 integers, there are 4,095 combinations!).  If you have a lot of numbers to consider then another approach would be to use a greedy algorithm.

SubsetSumλ = LAMBDA(integers, target_sum,
        LET(
            k, COUNT(integers),
            C, SUM(COMBIN(k, SEQUENCE(k))),
            bin, MOD(
                BITRSHIFT(SEQUENCE(C), SEQUENCE(, k, k - 1, -1)),
                2
            ),
            M, bin * TOROW(integers),
            check, BYROW(M, SUM) = target_sum,
            result, FILTER(M, check, "None"),
            result
        )
    );