What is the sum of the roots of the equation $(x - 5)^2 = 9$?
Knowing that $3$ is a root of $9$, we see that $x = 8,2$. Hence, the sum of the roots is $10$.

Alternatively, we can rearrange the equation so that we have $x^2 - 10x + 16 = 0$. Then, using the case of Vieta's formula for a quadratic, we again see that the sum of the roots is $\boxed{10}$.