let 'x' and 'y' be the numbers

two numbers multiply together to make -15

x*y = -15

they add together to make 2

x + y = 2 = > y = 2 - x

lets plug y = 2 - x into x*y = -15 we get

x(2-x) = - 15

by solving the above quadratic equation we find two roots

x1 = 5

x2 = -3

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For x = 5, y = 2 - 5 = -3

indeed 5*(-3) = - 15 and 5 + (-3) = 2

one solutions is x = 5, y = -3.

For x = -3, y = 2 - (-3) = 5

indeed (-3)*5 = - 15 and -3 + 5 = 2

second solutions is x = -3, y = 5.