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@Kimberly s
What you describe is not a 'paper', but evidently a film product.
one side was dark emulsion like film and the other flat like the backside of film.
That's odd because film doesn't have a dark emulsion. The emulsion on black & white film is generally off-white or pale grey. The backside can vary in tone from a dark grey or even black (on some specific types of film such as mammography x-ray film) to a pale grey.
I do think it's some kind of film or emulsion paper just can't find anything like it online.
'Emulsion' is the generic term for the light sensitive layer on a film or paper.
What you've got is evidently some kind of film.
It was bigger than 8x10 but much smaller than 11×14.
Sounds like it might be 32x40 cm, which is a common paper size in Europe (Bergger is French). It could well be something along the lines of what
@Rick A posted above, although that is different from your description:
* It comes in 8x10" and 11x14", but no sizes in-between (although someone might have cut smaller sheets from a bigger sheet or roll size)
* Before processing it's red on the backside and pale yellow on the emulsion/front side, so neither side would appear as 'dark' under typical darkroom safelight conditions.
However, since you mention it's an old/expired box you found, it's possible that it's a prior version of the product made/sold today.