Let 'x' and 'y' represent the two numbers.

x + y = -10

xy = -24

For x + y = -10 we get y = -10 - x

Plug y = -10 - x into xy = -24 and solve:

x(-10 - x) = -24

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x1 = 2

x2 = -12

For x = 2 we find y = -10-2, that is y = -12. So one solution is 2 and -12.

For x = -12 we find y = -10-(-12), that is y = 2. So the second solution would be -12 and 2.