jmc

We recognize that $|2x-36|=2|x-18|,$ so we get $$|x-20|=|x-18|.$$This means that, on the number line, $x$ is equidistant from $20$ and $18.$ Therefore $x$ must lie halfway between $20$ and $18,$ so $$x=\frac{20+18}{2}=\boxed{19}.$$