@Dario Saracchi, You can do some algebra before you do some code.
Define some constants:
d=AB*cos(alfa)-AC*cos(delta)
e=AB*sin(alfa)-AC*sin(delta)
a=BE, c=CE.
Then the equations
AB*cos(alfa)+BE*cos(beta)+CE*cos(gamma)-AC*cos(delta)=0
AB*sin(alfa)+BE*sin(beta)+CE*sin(gamma)-AC*sin(delta)=0
can be written
Now define 
and 
. Then the equations above can be written as
and . Then the equations above can be written as
Therefore 
, and therefore
, and therefore
which is one equation and one unknown. Try solving this with solve() or with vpasolve() or numerically with fzero(). Then you can compute 
and 
.
and .
