The sum of the real roots of the equation $|x-2{|}^2+|x-2|-2=0,$ is

We have, 

$\begin{array}{l}|x-2{|}^2+|x-2|-2=0\\ =\left(\right|x-2|+2)\left(\right|x-2|-1)=0\\ =|x-2|-1=0 [\because |x-2|+2+0]\\ =x-2=\pm 1\Rightarrow x=3,1\end{array}$

Sum of the roots = 4.