Spectral energy distribution (SED) fitting has been extensively used to determine the nature of the faint radio source population. Recent efforts have combined fits from multiple SED-fitting codes to account for the host galaxy and any active nucleus that may be present. We show that it is possible to produce similar-quality classifications using a single energy-balance SED fitting code, Prospector, to model up to 26 bands of UV$-$far-infrared aperture-matched photometry for $\sim$31,000 sources in the ELAIS-N1 field from the LOFAR Two-Metre Sky Survey (LoTSS) Deep fields first data release. One of a new generation of SED-fitting codes, Prospector accounts for potential contributions from radiative active galactic nuclei (AGN) when estimating galaxy properties, including star formation rates (SFRs) derived using non-parametric star formation histories. Combining this information with radio luminosities, we classify 92 per cent of the radio sources as a star-forming galaxy, high/low-excitation radio galaxy, or radio-quiet AGN and study the population demographics as a function of 150 MHz flux density, luminosity, SFR, stellar mass, redshift and apparent $r$-band magnitude. Finally, we use Prospector SED fits to investigate the SFR$-$150 MHz luminosity relation for a sample of $\sim$$133,000~3.6~\mu$m-selected $z<1$ sources, finding that the stellar mass dependence is significantly weaker than previously reported, and may disappear altogether at $\log_{10} (\mathrm{SFR}/M_\odot~\mathrm{yr}^{-1}) > 0.5$. This approach makes it significantly easier to classify radio sources from LoTSS and elsewhere, and may have important implications for future studies of star-forming galaxies at radio wavelengths.
Comment: 20 pages, 13 figures, accepted for publication in MNRAS