When electrons enter in a region where there is only magnetic field, then force exerted by the magnetic field will deflect the electron in a direction perpendicular to its motion and also perpendicular to the magnetic field.
Whereas in the presence of electric field, force exerted by the electric field is in a direction opposite to the direction of electric field. As a result, electron deflected by magnetic field is nullified by the deflection by electric field. As a result, electron moves undeflected.