Trigonometry · Hard problem

Surveying. Landmarks $P$ and $Q$ are $340$ m apart, with $Q$ east of $P$. From $P$ the bearing of a tower $T$ is N$52^\circ$E; from $Q$ the bearing of $T$ is N$18^\circ$W. Find the distances $PT$ and $QT$. Round to 2 decimal places (an exact answer is also accepted).