We analyze the spectra of high-temperature Fe XXIV lines observed by the Hinode/Extreme-Ultraviolet Imaging Spectrometer (EIS) during the impulsive phase of the X8.3-class flare on 2017 September 10. The line profiles are broad, show pronounced wings, and clearly depart from a single-Gaussian shape. The lines can be well fitted with kappa distributions, with values of kappa varying between ~1.7 and 3. The regions where we observe the non-Gaussian profiles coincide with the location of high-energy (ensuremath≈100-300 keV) hard X-ray (HXR) sources observed by RHESSI, suggesting the presence of particle acceleration or turbulence, also confirmed by the observations of nonthermal microwave sources with the Expanded Owens Valley Solar Array at and above the HXR loop-top source. We also investigate the effect of taking into account ensuremathkp̨a distributions in the temperature diagnostics based on the ratio of the Fe XXIII 263.76 and Fe XXIV 255.1 EIS lines. We found that these lines can be formed at much higher temperatures than expected (up to log(T[K]) ~ 7.8) if departures from Maxwellian distributions are taken into account. Although larger line widths are expected because of these higher formation temperatures, the observed line widths still imply nonthermal broadening in excess of 200 km s$^-1$. The nonthermal broadening related to HXR emission is better interpreted by turbulence than by chromospheric evaporation.