= Solution
Use a clean <Z boson> sample with final-state radiation, $Z\to e^+e^-\gamma$, and independently calibrated <electron> <four-momenta>. For measured $P=p_{e^+}+p_{e^-}$ and measured <photon> direction $\hat n_\gamma$, write $p_\gamma=E_\gamma(1,\hat n_\gamma)$. The known <Z boson> <mass> supplies
$$
M_Z^2=P^2+2E_\gamma(P^0-\mathbf P\cdot\hat n_\gamma),\qquad
\boxed{E_\gamma^{\rm pred}=\frac{M_Z^2-m_{ee}^2}{2(P^0-\mathbf P\cdot\hat n_\gamma)}.}
$$
Comparing the reconstructed <photon energy> with this prediction constrains its scale versus <energy>, detector position and conversion status. In practice fit the $e^+e^-\gamma$ <invariant mass> distribution, allowing for the physical <Z boson> <decay width>, detector response and backgrounds, instead of assigning every event exactly $M_Z$. Select final-state-radiation topologies: an initial-state-radiation <photon> is not part of the <Z boson> decay and generally does not satisfy the same mass constraint. The calibration applies over the populated <photon energy> range; extrapolation to still higher <energies> needs a validated response model.
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