The devil is in the details, of course. How much energy did the thing have? You can sort-of reconstruct an estimate based on how much light you saw on the ground and what angle you reconstructed the cosmic ray came in at. But--the light produced will depend a bit on the type of cosmic ray it was (proton, oxygen nucleus, iron nucleus, whatever). So you wind up with different numbers depending on what you think the particle was. The proportions of nuclei seen seem to vary with cosmic ray energy, too. We have no way of identifying what a cosmic ray was before it interacts. You can guess--for example there's a strong probability that the very highest energy particles were iron nuclei.
And the interactions in the atmosphere are random. If you happen to produce more muons early on in the shower, they'll carry more of the energy--but not show up any brighter in your detector. Result--you see less light, and think the original energy is lower than it really was. The only really good handles you have are statistical. When you see a lot of the cosmic rays you can get a distribution whose shape will tell you things about the original energy distribution--the outliers won't matter so much.
By the time the shower reaches ground level there's not much left but muons and photons (and neutrinos--lots of neutrinos).
FWIW, the highest energy core of a cosmic ray shower can sometimes (1/few-thousand events can have hundreds of muons) be surprisingly intense and narrow--10meters or even smaller. (muon bundles). And you, gentle reader, were probably struck by at least one cosmic ray shower muon while you were reading this.