Catalysis of the reaction: H+ + leukotriene E(4) + NADPH + O2 = 20-hydroxy-leukotriene E(4) + H2O + NADP+.
(7E,9E,11Z,14Z)-(5S,6R)-6-(cystein-S-yl)-5-hydroxyicosa-7,9,11,14-tetraenoate,NADPH:oxygen oxidoreductase (20-hydroxylating)