Generally all number systems use addition or multiplication to express numbers like - '12*3 + 6 for 42 in a base 12 system', '2 on the way to 50' or 'even 10+10+10+10+2 in some'. But, are there number systems which use subtraction like 10*5-8 (for an exemplar base 10 system), I know Ainu is close but not what I want to know about.
It's somewhat curious that both the Roman calendar and the Roman numerals used subtraction quite extensively; for neither is there any modern equivalent. For example, even the Advent sundays (which are defined as the four sundays before Christmas) are counted upwards; surely one could call them the fourth, third, second, first sunday (before Christmas) in that order instead, but that is not being done.
By contrast, the Roman calendar used subtractive counting throughout, being entirely based on months and 'signal post' days within each month (kalends, nones, ides) that are being counted 'towards'.
Likewise, in numerals, I, II, III, IV, V stand for the numbers one to five, with IV replacing the more straightforward IIII (which form is still used on clock faces, though). This is repeated with higher numbers, viz IX = 9, XC = 90, CM = 900 and so on. Be it said that usage appears to have been far from uniform, though; also, the Wikipedia article has many contradictory examples, and most are not from early (classical and pre-classical) times, so it's not immediately clear what the earliest forms were.
In both cases, the downward counting is so counter-intuitive to a modern observer that one is compelled to think there should have been a strong motivation for it to occur; maybe that motivation was in the number words of the early language; and, indeed @Yellow Sky cites duodētrīgintā ('2 from 30', 28 = 30 – 2) and ūndētrīgintā ('1 from 30', 29 = 30 - 1), which are quite naturally written out as IIXXX and IXXX in Roman numerals.
One could venture a wild hypothesis that in ancient Latium, there was a people with a language that used (partially) subtractive counting, vestiges of which system are to be found in their calendar and written number systems, akin to the 'twelve' vs 'thirteen', 'dozen' and 'gross', 'quatre-vingt-dix' of modern times that betray earlier duodecimal and vigesimal systems. The German Wikipedia article on Roman numerals somewhat rejects the link between written and spoken forms: "Die subtraktive Schreibung [...] stimmt aber mit [den Schreibweisen] nicht überein. Bei den lateinischen Zahlwörtern werden die Wörter für 1 und 2, aber nicht auch die für 10 und 100 subtraktiv verwendet und hierbei dann in der Regel auch nur den Vielfachen der 10 ab 20 (duodeviginti = 18, undeviginti = 19)"; OTOH, it admits that 'undecentum' = 99 (= IC) does sometimes appear in ancient sources.
The Yoruba language has a rather elaborate vigesimal (base-20) numeral system that involves both addition and subtraction and multiplication.
There are words for each of the decades; units in 1–4 are created by adding to these, while units in 5–9 are created by subtracting from the next decade. The odd decades are created by subtracting ten from the next even decade:
14=10+4; 15=20-5; 16=20-4; 50=20×3−10, 700=200×4−100; etc.
Also, Latin used subtraction in numerals. Among the numbers from 18 to 98, those that ended in 8 or 9 were formed by subtracting 2 and 1 from the following decade:
27: septem et vīgintī ('7 and 20')
28: duodētrīgintā ('2 from 30')
29: ūndētrīgintā ('1 from 30')