The photovoltaic (PV) single-diode model is the most widely used to characterize the behavior of a PV panel because it combines high precision with moderate difficulty. Lots of methods to obtain the model parameters use optimization techniques that require the resolution of the characteristic equation thousands of times; therefore, it is essential to calculate its solutions accurately but also in the shortest possible time. The objective of this article is to describe a new numerical strategy to solve the characteristic equation in a simple, fast and precise way. The main idea is based on a reparameterization of the Lambert equation which is closely related with the infinite power tower, and some well-known bounds of this tower will be used as seeds of numerical methods. This strategy is powerful for certain “small” values of the Lambert W function argument, but it is combined with another re-expression of the Lambert equation for the remaining “large” values. The proposed numerical strategy is so precise in very few iterations that it can be suitably transformed into an explicit formula. The results obtained have been compared with some of the best options in the literature and experimental results prove the power of the proposed methodology.