Answer
$$ r=\frac{z}{\cos\theta +\sin\theta} .$$
Work Step by Step
Since
$$ x=r\cos \theta,\quad y=r\cos \theta, \quad z=z,$$
then $ z=x+y $ takes the form
$$ z=r\cos\theta +r\sin\theta\Longrightarrow r=\frac{z}{\cos\theta +\sin\theta} .$$