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Let the numbers be x and y. x-y= 4 and xy= 96 which implies that y is 96/x. Substituting y in first equation x- (96/x) = 4 you get x square - 4x -96 = 0 which means that the root values are -12 and 8. X can't be negative so we consider the positive value which is 8. Substituting 8 in y= 96/x you get y as 12.
The numbers are 12 and 8.

x-y=4.....(i)

xy=96

y=96/x

putting this in (i)

x-96/x=4

⇒x²-4x-96=0

⇒(x-12)(x+8)=0

⇒x=12 or x=-8

so y=8 or y=-12