A family of E2 ubiquitin-conjugating enzymes (UBE2) that transfer ubiquitin from E1 ubiquitin-activating enzyme to the active site cysteine of the E2 enzyme. Then the ubiquitin is transferred from the E2 enzyme to the target protein by E3 ubiquitin ligases. The N-terminal extension found in UBE2E proteins may confer a strong preference for the monoubiquitination of substrates rather than polyubiquitination. [ ]