2020 AMC 10A Problem 5

The equation means $x^2-12x+34=2$ or $x^2-12x+34=-2$. The first gives $x^2-12x+32=0$, with roots $4$ and $8$. The second gives $(x-6)^2=0$, with root $6$. The sum of all real solutions is $4+8+6=18$. Thus, C is the correct answer.