That equality is often given as the definition of set different.
$(\forall x)[x\in B\vee x\notin B)$.
Your textbook must define $A\setminus B$ as $\{x:x\in A\wedge x\notin B(x\in\overline{B})\}$.
Which exactly what you are asked to prove. We do not prove definitions.
Therefore, either the question is faulty or you must give us more information.