#### Answer

$\color{blue}{\left\{5-\sqrt7, 5+\sqrt7\right\}}$.

#### Work Step by Step

Add $-18$ to both sides:
$x^2-10x=-18$
Add the square of one-half of the coefficient of $x$, which is $(\frac{-10}{2})^2=(-5)^2=25$, to obtain:
$x^2-10x+25=-18+25
\\(x-5)^2=7$
Take the square root of both sides to obtain:
$\sqrt{(x-5)^2}=\pm \sqrt{7}
\\x-5 = \pm \sqrt7$
Add $5$ to both sides:
$x=5 \pm \sqrt7$
Thus, the solution set is: $\color{blue}{\left\{5-\sqrt7, 5+\sqrt7\right\}}$.