Triangle Angle Relationships

In triangle DEF, angle D measures $30^{\circ}$ and angle E measures $x^{\circ}$. Angles D, E, and F form the interior angles of triangle DEF, and angle F is represented as $y^{\circ}$. The sum of the angles in any triangle is $180^{\circ}$.

Additionally, angle F is twice the measure of angle E. This relationship can be expressed as:

$$ y = 2x $$

Using this information, what is the measure of angle E?