A Vertex from the Euler Line

A triangle $ABC$ has vertices $A(-2,0)$ and $B(0,4)$, and its Euler line has equation $l:x+y-2=0$. (The Euler line joins the circumcenter $O$ and orthocenter $H$, with $2\overrightarrow{OG}=\overrightarrow{GH}$ where $G$ is the centroid.) Find the coordinates of vertex $C$.