In the diagram, $BE = 7$, $AB = 6$, and $[CBDA]=15.$ What is $[CDA]?$

[asy]
size(125);

pair C = (0,0);
pair D = (4,0);
pair EE = (2.5,0);
pair A = (2.5,4);
pair B = (2.5,2.5);

draw(A--C--D--cycle);
draw(C--B--D--cycle);
draw(A--EE, dashed);

draw(rightanglemark(B,EE,D,10));

dot(Label("$A$", A, N));
dot(Label("$B$", B, .5*NW));
dot(Label("$C$", C, SW));
dot(Label("$D$", D,SE));
dot(Label("$E$", EE,S));
[/asy]