Let [tex] x,y [/tex] be the two numbers. We have two pieces of information:
[tex] x-y=2 [/tex] (the difference between the two numbers is 2)
[tex] xy=224 [/tex] (their product is 224)
From the first equation, we can deduce [tex] x=y+2 [/tex]
If we plug this expression in the second equation, we have
[tex] xy = (y+2)y = 224 \iff y^2+2y-224 =0 [/tex]
If you solve this equation with the usual quadratic formula you get the solutions
[tex] y=-16,\quad y=14 [/tex]
So, you have the following couple of solutions, recalling that x is 2 more than y:
[tex] \begin{cases} x = -14\\y=-16\end{cases},\quad\begin{cases} x = 16\\y=14\end{cases}[/tex]
