Simulated current-voltage (I-V) characteristics of photovoltaic (PV) cells and modules are significant for the performance assessment, design and quality control, which are decided by the accurate determination of the intrinsic parameters of the devices. Commonly, a single-diode model is utilized to extract these parameters such as the ideality factor (n), series resistance (R-s), shunt resistance (R-sh), saturation current (I-o) and photo-generated current (I-lambda). Driven by this idea, a new mathematical manipulation was performed on the single-diode equation that yielded a non-linear formula of R-s. Later, Brents algorithm was used to precisely estimate R-s at every fine-tuned point of n, thereby all other parameters were determined. The set of parameters that provided the lowest root mean square error (RMSE) between the experimental and simulated I-V data were chosen to be optimum. The proposed Brents algorithm (BA) was shown outperform several recently reported computational and heuristic algorithms that were exploited to mine the single-diode model parameters for solar cells and modules with varied device temperatures and solar irradiation conditions.