The answer should be $14$
The edges in increasing order are
$\left \{ AE=1,ED=2,AD=3,DC=4,EC=5,AC=6,EB=7,DB=8,BC=9,AB=10 \right \}$
Applying Kruskal's algorithm:
We take $AE,ED$, we will not take $AD$ as $A$ and $D$ are already covered, then $DC$, then we will not take $EC$ and $AC$, then we will take $EB$
Edges in minimum spanning tree are : $\left \{ AE,ED,DC,EB \right \}$
Weight of minimum spanning tree = $1+2+4+7=14$