We report a study of the 3E excited-state structure of single negatively charged nitrogen-vacancy (NV) defects in diamond, combining resonant excitation at cryogenic temperatures and optically detected magnetic resonance. A theoretical model is developed and shows excellent agreement with experimental observations. In addition, we show that the two orbital branches associated with the 3E excited state are averaged when operating at room temperature. This study leads to an improved physical understanding of the NV defect electronic structure, which is invaluable for the development of diamond-based quantum information processing.