The difference of all the roots of the equation $|x^2-8x+15|-2x+7=0$  is

$$\begin{gathered} |x^2-8x+15|=\{\begin{array}{l}{x}^2-8x+15,x\le 3\text{ or }x\ge 5\\ -(x^2-8x+15),3<x<5\end{array} \\ Case 1: x\le 3\text{ or }x\ge 5 \\ {x}^2-8x+15-2x+7=0\Rightarrow x=5+\sqrt{3} \\ Case 2: 3<x<5,x^2-8x+15+2x-7=0\Rightarrow x=4 \\ Hence difference = 1+\sqrt{3} \end{gathered}$$