We address the problem of identifying an unknown portion \(\varGamma \) of the boundary of a d-dimensional ( \(d \in \{1, 2\}\) ) domain \(\varOmega \) and its associated Robin admittance coefficient, using two sets of boundary Cauchy data (f, g)-representing boundary temperature and heat flux–measured on the accessible portion \(\varSigma \) of the boundary. Identifiability results [9, 47] indicate that a single measurement on \(\varSigma \) is insufficient to uniquely determine both \(\varGamma \) and \(\alpha \) , but two independent inputs yielding distinct solutions ensure the uniqueness of the pair \(\varGamma \) and \(\alpha \) . In this paper, we propose a cost function based on the energy-gap of two auxiliary problems. We derive the variational derivatives of this objective functional with respect to both the Robin boundary \(\varGamma \) and the admittance coefficient \(\alpha \) . These derivatives are utilized to develop a nonlinear gradient-based iterative scheme for the simultaneous numerical reconstruction of \(\varGamma \) and \(\alpha \) . Numerical experiments are presented to demonstrate the effectiveness and practicality of the proposed method.