Triangle Inequality

Algebra Level 4

$E(x,y,z) = \dfrac {|x+y|}{|x|+|y|} + \dfrac {|y+z|}{|y|+|z|} + \dfrac {|z+x|}{|z|+|x|}$

The above expression is defined for non-zero reals $x, y, z$ .

If the minimum value of $E$ is $a$ and the maximum value is $b$ , find $a+b$ .