We present simulated J-band spectroscopy of red giants and supergiants with a 42m European Extremely Large Telescope (E-ELT), using tools developed toward the EAGLE Phase A instrument study. The simulated spectra are used to demonstrate the validity of the 1.15-1.22 micron region to recover accurate stellar metallicities from Solar and metal-poor (one tenth Solar) spectral templates. From tests at spectral resolving powers of four and ten thousand, we require continuum signal-to-noise ratios in excess of 50 (per two-pixel resolution element) to recover the input metallicity to within 0.1 dex. We highlight the potential of direct estimates of stellar metallicites (over the range -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 are also used to illustrate the potential for quantitative spectroscopy of red supergiants beyond the Local Volume to tens of Mpc. Calcium triplet observations in the I-band are also simulated to provide a comparison with contemporary techniques. Assuming the EAGLE instrument parameters and simulated performances from adaptive optics, the J-band method is more sensitive in terms of recovering metallicity estimates for a given target. This appears very promising for ELT studies of red giants and supergiants, offering a direct metallicity tracer at a wavelength which is less afffected by extinction than shortward diagnostics and, via adaptive optics, with better image quality.