We demonstrate very high–resolution photon spectroscopy with a microwave-multiplexed 4-pixel transition edge sensor (TES) array. The readout circuit consists of superconducting microwave resonators coupled to radio frequency superconducting-quantum-interference devices (RF-SQUIDs) and transduces changes in input current to changes in phase of a microwave signal. We used a flux-ramp modulation to linearize the response and avoid low-frequency noise. The result is a very high-resolution photon spectroscopy with a microwave-multiplexed 4-pixel transition edge sensor array. We performed and validated a small-scale demonstration and test of all the components of our concept system, which encompassed microcalorimetry, microwave multiplexing, RF-SQUIDs, and software-defined radio (SDR). We shall display data we acquired in the first simultaneous combination of all key innovations in a 4-pixel demonstration, including microcalorimetry, microwave multiplexing, RF-SQUIDs, and SDR. We present the energy spectrum of a gadolinium-153 (153Gd) source we measured using our 4-pixel TES array and the RF-SQUID multiplexer. For each pixel, one can observe the two 97.4 and 103.2 keV photopeaks. We measured the 153Gd photon source with an achieved energy resolution of 70 eV, full width half maximum (FWHM) at 100 keV, and an equivalent readout system noise of 90 pA/pHz at the TES. This demonstration establishes a path for the readout of cryogenic x-ray and gamma ray sensor arrays with more elements and spectral resolving powers. We believe this project has improved capabilities and substantively advanced the science useful for missions such as nuclear forensics, emergency response, and treaty verification through the explored TES developments.