jmc

The sum of the angle measures in a polygon with $n$ sides is $180(n-2)$ degrees. So, the sum of the decagon's angles is $180(10-2)=1440$ degrees. The polygon is regular, so all the angles have the same measure, which means each is $\frac{1440^{\circ }}{10}=144^{\circ }$. Similarly, the sum of the angles of a pentagon is $180(5-2)=540$ degrees, which means each angle in a regular pentagon has measure $\frac{540^{\circ }}{5}=108^{\circ }$.

Therefore, the desired difference is $144^{\circ }-108^{\circ }=\boxed{36^{\circ }}$.