  The Kepler planetary system consists of two exoplanets at similar separations
(0.115 & 0.128 AU), which have dramatically different densities. The inner
planet has a density consistent with an Earth-like composition, while the outer
planet is extremely low-density, such that it must contain a voluminous H/He
envelope. Such a density difference would pose a problem for any formation
mechanism if their current densities were representative of their composition
at formation. However, both planets are at close enough separations to have
undergone significant evaporation in the past. We constrain the core-mass, core
composition, initial envelope-mass, and initial cooling-time of each planet
using evaporation models conditioned on their present-day masses and radii, as
inferred from Kepler photometry and transit timing analysis. The inner planet
is consistent with being an evaporatively stripped core, while the outer planet
has retained some of its initial envelope due to its higher core-mass.
Therefore, both planets could have had a similar formation pathway, with the
inner planet having an initial envelope-mass fraction of $\lesssim 10\%$ and
core-mass of $\sim4.4$ M$_\oplus$, while the outer had an initial envelope-mass
fraction of order 15-30\% and core-mass $\sim7.3$ M$_\oplus$. Finally, our
results indicate that the outer planet had a long ($\gtrsim30$ Myr) initial
cooling-time, much longer than would naively be predicted from simple timescale
arguments. The long initial cooling-time could be evidence for a dramatic early
cooling episode such as the recently proposed "boil-off" process.
