Which two numbers add to 18 and multiply to - 63

The two numbers are 21, and negative 3. You know this because for the product to be a negative, one of your numbers have to be a negative. The factors of 63 are: 1 and 63. 3 and 21. 7 and 9

No matter what you do to 63 and 1, it is impossible to get 18.

For 3, and 21, 21 minus 3 is 18, and times is 63. So, 3 has to be a negative.