Solve it either Geometrically or Algebraically

Geometry Level 5

Let ${ a }_{ k }, { b }_{ k }, l \in { \Re }^{ + }$ and ${ a }_{ k }^{ 2 }+{ b }_{ k }^{ 2 } = { l }^{ 2 }$

$E = \cfrac { { a }_{ k }{ b }_{ k } }{ { a }_{ k }^{ 2 }+{ b }_{ k }^{ 2 }+({ a }_{ k }+{ b }_{ k })\sqrt { { a }_{ k }^{ 2 }+{ b }_{ k }^{ 2 } } }$

Find maximum value of $E$