We present radio observations of the tidal disruption event candidate (TDE) XMMSL1 J0740$-$85 spanning 592 to 875 d post X-ray discovery. We detect radio emission that fades from an initial peak flux density at 1.6 GHz of $1.19pm 0.06$ mJy to $0.65pm 0.06$ mJy suggesting an association with the TDE. This makes XMMSL1 J0740$-$85 at $d=75$ Mpc the nearest TDE with detected radio emission to date and only the fifth TDE with radio emission overall. The observed radio luminosity rules out a powerful relativistic jet like that seen in the relativistic TDE Swift J1644+57. Instead we infer from an equipartition analysis that the radio emission most likely arises from a non-relativistic outflow similar to that seen in the nearby TDE ASASSN-14li, with a velocity of about $10^4$ km s$^{-1}$ and a kinetic energy of about $10^{48}$ erg, expanding into a medium with a density of about $10^2$ cm$^{-3}$. Alternatively, the radio emission could arise from a weak initially-relativistic but decelerated jet with an energy of $sim 2times 10^{50}$ erg, or (for an extreme disruption geometry) from the unbound debris. The radio data for XMMSL1 J0740$-$85 continues to support the previous suggestion of a bimodal distribution of common non-relativistic isotropic outflows and rare relativistic jets in TDEs (in analogy with the relation between Type Ib/c supernovae and long-duration gamma-ray bursts). The radio data also provide a new measurement of the circumnuclear density on a sub-parsec scale around an extragalactic supermassive black hole.
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