Is this an acceptable way of writing the count of items in a sentence?

My father served in the logistics branch of Indian armed forces and he had a very particular style of representing the number of items of a certain object. For example, he would use this sentence:

Confirming the receipt of footballs (20 nos) and volleyballs (10 nos).
OR
Confirming the receipt of footballs (20 numbers) and volleyballs (10 numbers).

Of course I can also say, "Confirming the receipt of 20 footballs and 10 volleyballs", but it changes the emphasis that the sentence puts on the numbers.

I haven't seen this format used outside his military communication, though if I use it, people seem to understand it fine. Is there an internationally accepted way of writing numbers like this?

Guides often don't talk about parenthetical numbers. One military guide omits this concern entirely. So do more and less formal writing guides available online. They focus instead on when you spell numbers out. I could only find mention of this practice in an APS (American Physiological Association) Style Guide, which specifies writing units after a noun in parentheses in response to a concern about starting a sentence with a number:

You can rearrange a sentence so that the numbers do not appear first or insert a semicolon to connect it to the preceding sentence. For example, you can change:

…for five ocelots. 100-ml aliquots were then added to their cages.

to

…for five ocelots. Aliquots (100 ml) were then added to their cages.

More generally, shifting the number to a parenthesis after the noun rather than placing it before the noun feels fine. (I know I've seen it before without giving it much thought.) In the case of raw numbers rather than units like ml, saying "number" feels redundant: I would read "footballs (20)" as 20 footballs. However, it's possible that within your father's branch that they valued the redundant clarity of adding a unit (numbers or nos for short) for every number.

There's no international standard here. Instead, set a practice within a document and be consistent.