jmc

The given expression is undefined when the denominator equals zero. This occurs when $x^2-10x+16=0$. We use the fact that the sum of the roots of a quadratic equation $a{x}^2+bx+c=0$ is given by $-b/a$, so we see that the sum of the solutions to this equation must be $-(-10)/1=\boxed{10}$.