  KT Eridani was a very fast nova in 2009 peaking at V=5.42 mag. We marshal
large data sets of photometry to finally work out the nature of KT Eri. From
the TESS light curve, as confirmed with our radial velocity curve, we find an
orbital period of 2.61595 days. With our 272 spectral energy distributions from
simultaneous BVRIJHK measures, the companion star has a temperature of
6200$\pm$500 K. Our century-long average in quiescence has V=14.5. With the
Gaia distance (5110$^{+920}_{-430}$ parsecs), the absolute magnitude is
+0.7$\pm$0.3. We converted this absolute magnitude (corrected to the disc light
alone) to accretion rates, with a full integration of the alpha-disc model.
This accretion rate is very high at 3.5x10$^{-7}$ solar masses per year. Our
search and analysis of archival photographs shows that no eruption occurred
from 1928--1954 or after 1969. With our analysis of the optical light curve,
the X-ray light curve, and the radial velocity curve, we derive a white dwarf
mass of 1.25$\pm$0.03 solar masses. With the high white dwarf mass and
very-high accretion rate, KT Eri must require a short time to accumulate the
required mass to trigger the next nova event. Our detailed calculations give a
recurrence time-scale of 12 years with a total range of 5--50 years. When
combined with the archival constraints, we conclude that the recurrence
time-scale must be between 40--50 years. So, KT Eri is certainly a recurrent
nova, with the prior eruption remaining undiscovered in a solar gap of coverage
from 1959 to 1969.
