radicals - Solving Equations with Roots and Absolute Values

I'm preparing for the ACTM State contest, and I stumbled across this problem:

Which of the following is the sum of the tens digit and the units digit of the solution of the following equation?

$$15-2\sqrt{x-18} = 0.5 |x+14|-20$$

I know how to solve radical equations and absolute value equations, but I'm not familiar on how to solve an equation with both. Can anyone help me out?