Let us assume the two unknown numbers to be "x" and "y".
Then
xy = -240
x = - (240/y)
And
x + y = 8
Now let us put the value of x in the second equation. We get
x + y = 8
-( 240/y) + y = 8
y^2 - 240 = 8y
y^2 - 8y - 240 = 0
y^2 - 20y + 12y - 240 = 0
y(y - 20) + 12(y - 20) = 0
(y - 20) (y + 12) = 0
So we can see that the unknown number y can have two values and hence the unknown number will also have two values.
When
y - 20 = 0
y = 20
Then
xy = - 240
20x = - 240
x = -12
So we can see that when y is equal to 20 then x is equal to -12 and when y is equal to -12 then x is equal to 20. So the two numbers are 20 and -12.