The short answer is you can't, or at least not at all easily.
Your detector has only a single detection plane, and almost all muons are minimum ionizing, so you get essentially the same energy deposition from every muon (well, there is a factor from the angle of incidence the detection plane).
The usual mechanism for measuring the energy of a particle are
For charged particles, radius of curvature in a magnetic field. This will work for muons, but you need multiple detection planes and a high field. (This really gets momentum, so you need some kind of PID as well.)
Calorimetry of stopping particles. You need a detector with a lot of mass-per-unit-area in the direction of motion (and preferably segmented). For muons that'll have to be a lot of mass-per-unit-area.
Time of Flight between multiple detection planes. You need multiple detection planes. (Gives you velocity, so you need PID.)
Ring imaging of Cerenkov radiation (RICH). I suppose you could try this. You'll need a modified lens and a very sensitive CCD. Not sure how you are going to trigger it, though. (Velocity again.)
There are a few special tools like transition radiation. Not something I know much about.
With cosmic rays the bulk of the impinging particles are muons, so you can just assume the species instead of doing a proper job of PID.
A RICH modification would presumably have a single element bi-planer lens made out of some very clear glass or plastic and have the lens cover permanently attached (because you don't want outside light). You'll choose the index of refraction and distance from the focal plane according to the size of the focal plane detector and the slowest muon you want to image.
I don't know enough about modern digital cameras to know if they can be self-triggering. Maybe it is enough to simply take timed exposures without triggering and do a counting experiment.
This is interesting enough that I'm going to look into it further.
Not only have I looked into the RICH modification, I set some students working on it, and we appear to have gotten it working briefly. Then we broke the camera.
There are several challenges:
Detector sensitivity. Few camera detectors have significant single-photon QE even at the highest ISO equivalent level. Worse the data provided by the manufacturers can not be easily and reliably converted to these values.
Detector size. Modern camera detectors have been getting ever smaller except in expensive models.
Optics geometry and radiator selection. The device necessarily has a forward geometry, and total internal reflection is a issue for getting the light to the focal plane (for muons near the 1 GeV peak in frequency). There are only a couple of commercially available solids that will do (plus areogels). Liquids and gasses are possible, but must be contained (and for gasses have their pressure regulated).
Thicker radiators will generate more total light, but too think and the signal will cover too much of the detector surface for reliable ring-parameter measurements.
Also getting a good alignment between the radiator and the focal plane is hard. More, some manufactures deliver their cameras with thin-films over the focal plane detector.
Dark noise. It might seem obvious to run long frame rates to increase the odds of getting a hit, but dark noise starts to accumulate. As each event is very short you may be better taking a lot of short frames and knowing that you will have to discard a lot of data. In any case, you will also want to acquire a reliable dark-noise measurement to use in subtraction.
We have (probably) one event at this point, but one of my students did present the work that we have at the April 2015 APS meeting in Baltimore. I'll update this post when I can actually prove that what I have is a Cerenkov event.