Proving the undecidability of a language knowing the language of polynomials evaluating to 0 is undecidable
Yes like you say, you have to show that an algorithm that solves $E$ can be used to solve $D$. 

A practical approach is to give a polynomial $p_E$ for every polynomial $p$ such that $p$ evaluates to $0$ iff $p_E$ evaluates to a prime number.