Residual stresses are ubiquitous across industrial processes and biological systems, ranging from quenching and welding to tissue remodeling. Their impact is critical; neglecting these stresses can lead to suboptimal designs and catastrophic structural failure. Despite their importance, experimental estimation of residual stresses remains spatially restricted and resource-intensive. Conversely, forward numerical simulations are often constrained by the complexity of constitutive models and the extensive phenomenological parameters required as inputs. In this study, we present a novel family of inverse formulations capable of reconstructing residual stress fields with high fidelity. We demonstrate that residual stress recovery is achievable for both linear and nonlinear solids, maintaining independence from the underlying physics of the stress source. Our results show accurate reconstructions derived from opening tests across diverse applications. This hybrid numerical-experimental approach offers a robust framework to enhance the quantification of residual stress fields within existing experimental protocols.