$\displaystyle E:= \{m: 2m, m \in \mathbb{N}\}$

$\displaystyle U:= \{n: 2n+1, n \in \mathbb{N}\}$

Proof by contradiction:

assume $\displaystyle E_1+E_2=U$

$\displaystyle \Rightarrow 2m_1+2m_2=2n+1$

$\displaystyle \Rightarrow 2m_1+2m_2-1=2n$

$\displaystyle \Rightarrow \nexists m \in \mathbb{N}: 2\mid(2m_1+2m_2-1)$

This contradicts the assumption, therefore E_1 + E_2 = E_3