Hint

This gives us the interval $(-8,22)$ except at $x=2$

I think that we must have $0<\frac{20}{x+18}<1$, and $1\le \frac{x+18}{20}<2$ or viceversa, it is true? From $0<\frac{20}{x+18}<1$, and $1\le \frac{x+18}{20}<2$, we get the intervalfrom $x$ is $(2,22)$. And we must solve the "viceversa", we get the interval $(-8,2)$, so the resultis $(-8,22)$ excepting $x=2$