Design an exhaustive search algorithm for this problem:

Suppose n positive integers are given to you. Partition these numbers into two disjoint subsets in a way that both subsets have the same total sum. Try to make sure that your algorithm works for all possible inputs, you should consider cases when the input has no solutions and return appropriately.

Note: If you need to generate all permutations or subsets, for example, you do not need to write an algorithm for the generation part. You can just write generate all permutations.