The sum of two numbers is 25 and their difference is 11. What is the larger of the two numbers?
Let $x,y$ be the two numbers, $x>y$. Then $x+y=25$ and $x-y=11$, thus:

$x=\frac{1}{2}\left((x+y)+(x-y)\right)=\frac{1}{2}(25+11)=\boxed{18}$.