$ABCD$ be an isosceles trapezium such that $AD=BC$, $AB=5$ and $CD=10$. A point $E$ on the plane is such that $AE \perp EC$ and $BC=EC$. The length of $AE$ can be expressed as $a \sqrt{b}$ where $a$ and $b$ are integers and $b$ is not divisible by any square number other than $1$. Find the value of $(a+b)$.