18. (12 points) In $\triangle A B C$ , the sides opposite to angles $A , B , C$ are $a , b , c$ respectively. Given that When $t = 0$, $S = 3$; when $t = \pm 1$, $S = 4\sqrt{2}$. Therefore, the area of quadrilateral $ADBE$ is $3$ or $4\sqrt{2}$.
Solution:
18. (12 points)\\
In $\triangle A B C$ , the sides opposite to angles $A , B , C$ are $a , b , c$ respectively. Given that
When $t = 0$, $S = 3$; when $t = \pm 1$, $S = 4\sqrt{2}$.
Therefore, the area of quadrilateral $ADBE$ is $3$ or $4\sqrt{2}$.