An algebra problem by Zulqarnain Ansari

other ways:

let the first number is A and the second number is B, so:

${ \left( A-B \right) }^{ 2 }={ A }^{ 2 }+{ B }^{ 2 }-2AB=36$

${ A }^{ 2 }+{ B }^{ 2 }=36+2AB=260$

then

${ \left( A+B \right) }^{ 2 }={ A }^{ 2 }+{ B }^{ 2 }+2AB=260+224=484$ $A+B=\sqrt { 484 } =\boxed{22}$

so the anwer is 22

Let x be one number, then x + 6 since their product is 112, therefore x(x + 6) = 112 That is x^2 + 6x - 112 = 0 gives x =8 and x = 14