The points $A$, $B$, $C$, $D$, $E$ lie on the circle with center $F$, and $\overline{EB}$ is a diameter. The central angles around $F$ must sum to $360°$.

The given central angles are:

$\angle AFB = 90°, \quad \angle BFC = 18°, \quad \angle CFD = 108°$

The remaining central angles satisfy:

$\angle DFE + \angle EFA = 360° - 90° - 18° - 108° = 144°$

The arc $\overset{\frown}{DEA}$ (from $D$ to $E$ to $A$, not passing through $B$ or $C$) corresponds to the sum of central angles $\angle DFE + \angle EFA$:

$\overset{\frown}{DEA} = 144°$