The is no fast way. The numbers are not defined in terms of each other. That means that there is no equation that can be used to express the relationships.

However, there are only 10 numbers, the solution can be calculated very quickly.

You need to make sure that all numbers are pair with all other sets of numbers. If the sum of a subset equals x, then it is kept. Otherwise the values less than x and greater than x are discarded.

Combinations/Permutatons:

A computer program could be used to take all of then numbers 1 at a time, 2 at at time, 3 at at time, etc. Summing the group to determine if it is equal to X.

Do you have specific values with which to work or is the question general purpose?