In this Communication, we consider a generalised Tavis–Cummings model when the damping process is taken into account. We show that quantum dynamics governed by non-Hermitian Hamiltonian exactly solvable using Quantum Inverse Scattering Method, and Algebraic Bethe Ansatz. The leakage of photons described Lindblad-type master equation. diagonalised state vectors, which are elementary symmetric fu...