  Flare loops form an integral part of eruptive events, being detected in the
range of temperatures from X-rays down to cool chromospheric-like plasmas.
While the hot loops are routinely observed by the Solar Dynamics Observatory's
Atmospheric Imaging Assembly (SDO/AIA), cool loops seen off-limb are rare. In
this paper we employ unique observations of the SOL2017-09-10T16:06 X8.2-class
flare which produced an extended arcade of loops. The Swedish 1-m Solar
Telescope (SST) made a series of spectral images of the cool off-limb loops in
the Ca II 8542 \r{A} and the hydrogen H$\beta$ lines. Our focus is on the loop
apices. Non-LTE spectral inversion is achieved through the construction of
extended grids of models covering a realistic range of plasma parameters. The
Multilevel Accelerated Lambda Iterations (MALI) code solves the non-LTE
radiative-transfer problem in a 1D externally-illuminated slab, approximating
the studied loop segment. Inversion of the Ca II 8542 \r{A} and H$\beta$ lines
yields two similar solutions, both indicating high electron densities around $2
\times 10^{12}$ cm$^{-3}$ and relatively large microturbulence around 25
kms$^{-1}$. These are in reasonable agreement with other independent studies of
the same or similar events. In particular, the high electron densities in the
range $10^{12} - 10^{13}$ cm$^{-3}$ are consistent with those derived from the
SDO's Helioseismic and Magnetic Imager white-light observations. The presence
of such high densities in solar eruptive flares supports the loop
interpretation of the optical continuum emission of stars which manifest
superflares.
