Well ... almost.

The Subset Sum Problem asks if there is one solution.

But the OP asks to "list all possible combination of numbers"

Algorithm wise that's a huge difference, because one can often optimize searching for a single solution, while happily ignoring the rest. °

And that's also why I'm hesitant solving this, you can easily show that the solution space of all possible combinations will explode quickly, in a way that already the time needed to print them out will take an eternity.

I.O.W. such problems don't make much sense, unless you are singling out a single (or a few) solution which are optimal regarding a second value-function.

°)The Knapsack Problem will also demand to optimize a second "value" function and only require the "weight" to be less or equal the "target". It's a generalization of Subset Sum b/c if you choose the weight as value, the equal case - if it exists - will be maximal.