Answer
$9$ and $11$.
Work Step by Step
Let the smaller integer be $x$.
The larger integer is $x+2$.
From question we have.
$\Rightarrow (x)(x+2)=(x+2)^2-22$
Clear the parentheses and apply the distributive property.
$\Rightarrow x^2+2x=x^2+4x+4-22$
Add $-x^2-4x$ to both sides.
$\Rightarrow x^2+2x-x^2-4x=x^2+4x+4-22-x^2-4x$
Simplify.
$\Rightarrow -2x=-18$
Divide both sides by $-2$.
$\Rightarrow \frac{-2x}{-2}=\frac{-18}{-2}$
Simplify.
$\Rightarrow x=9$
Smaller integer is $9$.
Larger integer is $9+2=11$.
