Maximizing energy yield (EY) - the total electric energy generated by a solar cell within a year at a specific location - is crucial in photovoltaics (PV), especially for emerging technologies. Computational methods provide the necessary insights and guidance for future research. However, existing simulations typically focus on only isolated aspects of solar cells. This lack of consistency highlights the need for a framework unifying all computational levels, from material to cell properties, for accurate prediction and optimization of EY prediction. To address this challenge, a differentiable digital twin, Sol(Di)$^2$T, is introduced to enable comprehensive end-to-end optimization of solar cells. The workflow starts with material properties and morphological processing parameters, followed by optical and electrical simulations. Finally, climatic conditions and geographic location are incorporated to predict the EY. Each step is either intrinsically differentiable or replaced with a machine-learned surrogate model, enabling not only accurate EY prediction but also gradient-based optimization with respect to input parameters. Consequently, Sol(Di)$^2$T extends EY predictions to previously unexplored conditions. Demonstrated for an organic solar cell, the proposed framework marks a significant step towards tailoring solar cells for specific applications while ensuring maximal performance.