Most Essie nail polishes do not require UV or LED light to dry or cure. Essie nail polishes are regular air-dry nail polishes that dry on their own when exposed to air.
However, Essie does have a line of gel-like nail polishes called Gel Couture that requires a special topcoat and a LED lamp for curing. If you're using regular Essie nail polish, you do not need UV or LED light for drying or curing.