I know the coordinates of points E and Q, so I know their euclidean distance L. I'm looking for the point W with coordinates (a,b) related to other known values?

I know the coordinates of points E and Q, so I know their euclidean distance L. I'm looking for the point W with coordinates (a,b) related to other known values?

I'll assume you know $\theta$, the coordinates $(x,y)$ of $Q$, and $r$. The angle of rotation from a vertical line through $Q$ to $\overline{QW}$ is also $\theta$, so if we take the point that is $r$ above $Q$ and rotate it by $\theta$ about $Q$, we'll get $W$. That means $$W=(a,b)=(x-r\sin\theta,y+r\cos\theta).$$