There isn't an unique solution to these equations. For example, for the first one, you may pick two arbitrary positive number, and fix the third so that the sum is -20.
Say that you choose 4 and 26. Their sum is 30. To reach -20, the third number must be -50.
So, 4, 26 and -50 are three numbers that sum to -20 and don't have all the same sign.
Similarly, for the second requirement, pick two negative numbers, and adjust the third.
If you choose -3 and -2, their sum is -5. So, the third must be 15. In fact, -3, -2 and 15 are three numbers that sum to 10 and don't have all the same sign.
