I recently (as in last week) purchased a broken TI-2500 off Ebay, which a little soldering and new batteries fixed up in half an hour. Beyond the obvious novelty of holding a nearly forty year old calculator that uses its 7-segment VRAM as memory, I've also become very interested in what particular model this calculator is, because it doesn't actually resemble any hardware revision that's documented on datamath.org or vintagecalculators.com. It's very puzzling. it has the label shape as though it's Version 1, but not the removable battery cover. The inside had no battery tray, only a set of four rechargeable 1.2v AA batteries soldered together and to the calculator. Does anyone know what version this is? I'll post the back of it below.

Also, a fun fact I discovered about this calculator is that it actually contains a wooden component!

Edit: Just noticed that it has a CE button, not a CE/D button, meaning it is not affiliated with version 1.

From what I can tell, yours looks like a mash up of version 1 and 2. I think the 001-E means it's a hardware revision E which may be an early model of the version 2 since the back plate and serial number length matches up with V2 but V1 has the revision labeled in that area, but different.
V1 on left, V2 on right

I wish the V2 image was higher resolution.

I checked the back of my TI-2500 and my Serial Number is 2500-41405 with Rev. D.

Woah. A real rare boi.