The color of their shield will dictate what weapon damage type will do more damage against them (shields only). It will also tell you a damage type for that mission before you start it. So you can have a general weakness for the mission and also specific weaknesses for enemies' shields. For heroic tier missions, there will be skulls with elemental modifiers on them. Arc Burn, Void burn and Solar Burn. Whichever skull is active, that element has a 300% damage increase. Be sure to check which skulls are active and equip the corresponding heavy and special weapon.