Let $ L = \{ \langle M \rangle : L(M) = \Sigma^* -\{\epsilon\} \}$, Show that $L\notin RE$
Hint: Let $L_{\Sigma^*}$ the language of descriptions of Turing machines halting on all inputs. Choose some computable surjective mapping from $\Sigma^+$ to $\Sigma^*$, and use it to reduce $L_{\Sigma^*}$ to $L$. Since $L_{\Sigma^*}$ is neither RE nor coRE, it follows that the same holds for $L$.