[ Tangents touching circles ]

On the base $AB$ of the isosceles triangle $ABC$, a point $E$ is taken, and circles are inscribed in triangles $ACE$ and $ECB$, touching the segment $CE$ at points $M$ and $N$. Find the length of the segment $MN$, if the lengths of segments $AE$ and $BE$ are known.
According to problem 3.2. $C M=(A C+C E-A E) / 2$ and $C N=(B C+C E-B E) / 2$. Considering that $A C=B C$, we get $M N=| C M-C N|=| A E-B E \mid / 2$