Conservation of Energy in photon exchange between two atoms

Consider a hydrogen atom, A, in the first excited state placed at a small distance from another hydrogen atom, B, in the ground state. Now, when A drops down to the ground state, it emits a photon which must have an uncertainty in its energy/frequency due to the energy-time uncertainty relation. And when this photon is absorbed by the other atom, B, the energy transferred also much have an uncertainty by the same principle. So how do we account for conservation of energy, when both the processes of emission and absorption have an inherent uncertainty in them? Is it not possible that there are small violations of energy conservation in each experiment, and that conservation works only on average over many experiments?