  The recent discoveries of Swift J1644+57 and J2058+05 show that tidal
disruption events (TDEs) can launch relativistic jets. Super-Eddington
accretion produces a strong radiation field of order Eddington luminosity. In a
jetted TDE, electrons in the jet will inverse-Compton scatter the external
radiation field from the accretion disk and wind. Motivated by observations of
thermal optical-UV spectra in Swift J2058+05 and several other TDEs, we assume
the spectrum of the external radiation field intercepted by the relativistic
jet to be blackbody. Hot electrons in the jet scatter this thermal radiation
and produce luminosities 10^45-10^48 erg/s in the X/gamma-ray band.
  This model of thermal plus inverse-Compton radiation is applied to Swift
J2058+05. First, we show that the blackbody component in the optical-UV
spectrum most likely has its origin in the super-Eddington wind from the disk.
Then, using the observed blackbody component as the external radiation field,
we show that the X-ray luminosity and spectrum are consistent with the
inverse-Compton emission, under the following conditions: (1) the jet Lorentz
factor is ~5-10; (2) electrons in the jet have a powerlaw distribution with
minimum Lorentz factor ~1 and powerlaw index p = 2.4; (3) the wind is mildly
relativistic (Lorentz factor >~1.5) and has isotropic-equivalent mass-loss rate
~5 M_sun/yr. We describe the implications for jet composition and the radius
where jet energy is converted to radiation.
