"TEA" is the acronym for triethanolamine, a quaternary ammonium compound. Triethanolamine reacts easily with fatty acids to form triethanolamine soaps and is used as a basic component in soaps and other cosmetic products. "Oleyl" refers to oleyl alcohol (octadec-9-en-1-ol - an unsaturated fatty alcohol) as the alcoholic part of a compound, sulfates are salts or esters of sulfuric acid.
TEA-oleyl sulfate is a substance used in cosmetic formulations where it acts as a surfactant (washing-active substance; improves the even distribution of the products during application), emulsifier (surface-active substance used in cosmetic preparations as an auxiliary agent to combine 2 immiscible liquids - e.g. oil and water - to form an emulsion) and foaming agent (increases the foaming and improves the volume, structure and durability of the foam).