#### Answer

$x=\{3,11\}$

#### Work Step by Step

"The difference between a number and 7" is written as $x-7$.
The equation can be written as:
$(x-7)^2=16$
Take the square root of each side.
$\sqrt{(x-7)^2}=\sqrt{16}$
Simplify.
$x-7=\pm4$
Add 7 to each side.
$x-7+7=\pm4+7$
Simplify
$x=4+7$ or $x=-4+7$
$x=11$ or $x=3$
State as a solution set.
$x=\{3,11\}$