Answer
$r=\frac{2}{\cos\theta+\sin\theta}$.
Work Step by Step
To convert from polar to rectangular coordinates we use $x=r\cos\theta$ and $y=r\sin\theta$. To convert from rectangular to polar coordinates, we use $r=\pm\sqrt{x^2+y^2}$, $\tan\theta=\frac{y}{x}$, but aware of which quadrant the point lies in.
Hence here $x+y=2\\r\cos\theta+r\sin\theta=2\\r(\cos\theta+\sin\theta)=2\\r=\frac{2}{\cos\theta+\sin\theta}$.