My response will be based on the assumption that you mean triangle QWE rather than DeltaQWE and also that we are working in a plane.

Since the interior angles sum to 180, that means angle W=45 and we have an isosceles right triangle. With that, knowing one leg, EW=7, guarantees the other leg is congruent so WE=7 as well.

In a 45-45-90 triangle the hypotenuse is always longer than the legs by a factor of sqrt(2), ergo QW=7sqrt(2)