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We present simulated J-band spectroscopy of red giants and supergiants with a42m European Extremely Large Telescope (E-ELT), using tools developed towardthe EAGLE Phase A instrument study. The simulated spectra are used todemonstrate the validity of the 1.15-1.22 micron region to recover accuratestellar metallicities from Solar and metal-poor (one tenth Solar) spectraltemplates. From tests at spectral resolving powers of four and ten thousand, werequire continuum signal-to-noise ratios in excess of 50 (per two-pixelresolution element) to recover the input metallicity to within 0.1 dex. Wehighlight the potential of direct estimates of stellar metallicites (over therange -1<[Fe/H]<0) of red giants with the E-ELT, reaching out to distances of~5 Mpc for stars near the tip of the red giant branch. The same simulations arealso used to illustrate the potential for quantitative spectroscopy of redsupergiants beyond the Local Volume to tens of Mpc. Calcium tripletobservations in the I-band are also simulated to provide a comparison withcontemporary techniques. Assuming the EAGLE instrument parameters and simulatedperformances from adaptive optics, the J-band method is more sensitive in termsof recovering metallicity estimates for a given target. This appears verypromising for ELT studies of red giants and supergiants, offering a directmetallicity tracer at a wavelength which is less afffected by extinction thanshortward diagnostics and, via adaptive optics, with better image quality.

Stellar metallicities beyond the Local Group: the potential of J-band spectroscopy with extremely large telescopes