$\emptyset$ \ $\emptyset = \emptyset$ solution emptyset minus the emptyset solution? Is there a solution? $\emptyset$\ $\emptyset = \emptyset$ is the only solution I could conjure when thinking of the solution to this problem.

The empty set contains no elements, hence what you are doing is removing no elements from some set, say $A$, which yields $A$, i.e. $A\backslash \emptyset = A$.

Now take $A$ to be the empty set.