IMO E... idiom is Both...And.

A) looks okish.. not sure about the "as well" at the end.
B) the correct idiom is "both of X and Y" .. here, "both of X and also of Y" is redundant & wrong
C) the correct idiom is "both of X and Y" .. here, "both of X and also from Y" is redundant & wrong
D) both of X, but also Y is just horrible. SOS.
E) the correct idiom is "both of X and of Y" .. here, "both of X and also from Y" is redundant & wrong

looks like A is the best answer

A.) Seems to be correct among all of these..
B.) "both of X and also of Y" is redundant & wrong
C.) Same as B.
D.) Wrong idiom..Both X and Y is the correct idiom.
E.) Both ..as well redundant. and incorrect idiom

I would go with A..

Most recovering heroin addicts seek to be free of drug dependency and others' prejudicial treatment as well.

(A) of drug dependency and others' prejudicial treatment as well. - Parallelism Error

(B) both of drug dependency and also of prejudicial treatment. - Incorrect Idiom

(C) both of drug dependency and also from prejudicial treatment. - Incorrect Idiom

(D) both of drug dependency but also from prejudicial treatment. - Incorrect Idiom

(E) both of drug dependency and of prejudicial treatment as well. - Correct

+for E