We can substitute $x$ for $\frac{18+2y}{5}$. So we have $y=2(\frac{18+2y}{5} -7.$ That simplifies to $y=\frac{36+4y}{5}-7$, or $y+7=\frac{36+4y}{5}.$ We don't like fractions, so therefore, we can multiply the whole equation by $5$, to get $35+5y=36+4y$, or $y=\boxed{1}.$ To solve for $x$, we can substitute: $$x=\frac{18+2y}{5}=\frac{18+2}{5} = \frac{20}{5}=\boxed{4},$$ so $(x,y)=(4,1).$
.
