Take a few pictures from a few different angles, then try sanding with really fine grit sandpaper. Sand lightly and take off the rust and extra layers of paint very slowly. Keep taking pictures as you go and you'll get an idea of whether or not its layered markings or not.
As stated above, the passenger front bumper will be the overall parent unit, the left bumper will be company/troop and a number denoting its role in that company. This is a rule of thumb. Different units have different SOP's and units within units can have different SOP's as well so there's a wide variation. Not to mention what the hell the Nasty Girls do when they get the hand-me-down trucks and spray their markings over the RA markings if they haven't already been defaced at the refurb depot.
I couldn't recover the markings on mine. The front bumper was swapped off of another truck by the seller 25 years ago and the rear bumperettes were so gouged up by hooks and chains over the years that I could only recover two letters that led me nowhere. As a result, I went with the markings my unit had on our HMMWVs back when I was in. I'll use that as an example.
The unit will read left to right, like a sentence. It will start with the largest unit and work its way down to the individual truck number.
I have stenciled: "101ABN/1-32CAV" on the left and "A-34" on the right. Obviously 101st Airborne Division and 1st Squadron, 32nd Cavalry Regiment. The brigade number is skipped. That was our SOP. If you knew the 32nd was in 1BCT, then you saved money on spraypaint and AM General didn't have to make the trucks any wider than they already were. On the driver side you now have "A-34" - A Troop, 3rd Platoon, 4th Truck. (and obviously, erroneous for a 1950's vehicle as that unit was technically still an armored unit that hadn't been attached to the 101st yet. Sue me.)
Now this is how it was in my unit, and I know most other units do this too- but not all will have the same SOP for truck numbering. The 4th truck will be the platoon sergeant's vehicle. A-31 would be the same unit but be the platoon leaders truck. Corresponds with the radio call signs. Most three-platoon units use the Red, White and Blue for 1st, 2nd and 3rd platoons. So a radio message from Blue 1 to Blue 4 would be the platoon leader in the 1 truck calling the platoon sergeant in the 4th truck. if its part of the headquarters company or troop you'll see HQ, HHC or HHT If its a battalion or squadron level vehicle you'd see "HQ" in place of the company or troop letter identifier. 6 being the battalion commander, 5 being the battalion XO, 8 being the master sergeant at the motorpool who has never, ever ridden in that truck, 7 being the CSM unless the "HQ-7" reads as "A-7" in which case you're in deep crap because you've accidentally walked up on the 1SG's truck and he's looking for a volunteer to lead a mine clearing patrol and you haven't shaved all day. As most 3/4 tons weren't used as front line combat vehicles, you'll see most M37's attached to HQ for mundane uses like mail or ash and trash, hauling ammo to the range so the new privates can crossfire each others targets under a blazing sun. Its all a repeating pattern. And right as you figure it all out, you'll realize that you still can't decipher a damn thing because everything I just told you probably won't apply to the unit(s) that had your truck in the past.
That's how it is in a light cavalry unit, anyway. In an engineer unit or a support unit, you'll have more vehicles for specialized roles and cargo hauling so the numbering system can grow beyond what I stated.
So the real trick here is to get an idea of the parent unit info and start googling images of their vehicles (if possible) from the time period to get an idea of what you are looking for. Once you have a handle on what to expect on the bumper, it may be easier to decipher layers of paint and letters overlapping. I'd just keep taking photos and sand, take more photos as the process unfolds, sand more etc. Eventually you may be able to uncover discernable markings.
Since you've got a dump truck and the rear bumperette seems to say ENG, I'd do my best to figure out which number proceeds the "ENG" letter to identify which Engineer unit your truck was assigned to. See if you can get the rear bumperette info to correlate with stuff on the front bumper and vice versa. If you can use one to decode the other, you're already that much further along than I ever got.