jmc

Let the two numbers be $x$ and $x+2$, where $x$ is even. We want to find $x+(x+2)=2x+2$, and we are told that $(x+2{)}^2-x^2=60$. This last equation can be factored as a difference of squares: $(x+2+x)(x+2-x)=(2x+2)(2)=60$. It follows that $2x+2=60/2=\boxed{30}$.