Your title question and your concluding question are quite different, and it depends.
In what war would one modern military vehicle make a difference?
First, many small things "make a difference" and these combine to lead to the outcome. Sometimes, a single contemporary tank or a handful of commandos has made "a difference".
When you ask "would ... make a difference" though, while any time-travelling technology would make some difference, what that difference would actually be, depends entirely on the circumstances of what happens to it.
This is an old type of fantasy question, and it tends to imply many assumptions in order to indulge the question, which ignore the kinds of questions which would actually determine the outcome. I.e. these questions tend to be imagining history as it was, only a Challenger II lines up with Napoleon to help him win at Waterloo, and the crew speaks French and the French army isn't utterly confused by this, and the Challenger II crew knows what is going on and what to do, and nothing breaks down, and the enemy army doesn't just panic and hide until they figure out what's going on, and then have a spy assassinate, bribe or seduce the wizards running the magical war engine. The "realistic" answer is you would probably be distrusted and captured before getting to join in a battle.
Even assuming that the people operating the tank are all linguist/historians who have a master plan for joining one side in the war without being captured, and all goes well, the next major deciding factors realistically are going to again be not-very-fantasy-soothing considerations like fuel and ammo limits, malfunctions and repair, lack of roads, breakdowns, and the use of improvised explosives, fire and smoke, or other mundane obstacles. Also the enemy army is probably going panic and rout, and though you can can probably turn what was a pitched battle into a rout, what historically was the pitched battle may turn into something else as the victims try to understand what happened and do something other than face your tank in battle.
So it's impossible to say what "would" happen. Something unpredictable. In a recent enough war (as far back as World War II), it would just tilt the scales in one battle until something immobilized the tank or it ran out of fuel or ammunition. After all, in World War II, there were many cases where one side had severe armor superiority. Often one side had no good way to defeat enemy tanks, and/or had no tanks of their own. It was a key advantage, but not always decisive, even for relatively small battles. The Challenger II is extremely powerful, but it's only one tank, with limited supplies, and it can be immobilized by mines or high explosives or abatis or a lucky HE round. The chaingun is wicked, but it and the main gun could both eventually be disabled by even 1939 weaponry, even if the tank's armor couldn't be penetrated.
Even in World War I, the Challenger II might do a lot of damage in one battle, but many conventional weapons also did a lot of damage in World War I. Particularly in the trenches on the Western Front, the best the tank might do would be equivalent to one successful attack, or one failed attack by the enemy, but then your tank would presumably be used up. The least it might do is get immobilized by the ridiculous terrain and/or all the mines and high explosives, before it did a whole lot of damage. Maybe if you also brought-back-in-time maps of the other side's rear deployments on a certain date (another possible time travel question), and drove over and blew up all their ammo dumps or something, you might be able to set up your allies for a decisive breakthough.
As for your concluding question:
when is the last war that could be won or lost by the addition or subtraction of one modern tank?
Again mincing words, I would say you could maybe possibly tip the scales of World War I if you planned quite well and acted unconventionally, as I suggested above.
Before then, I think you could turn the tide of just about any one battle before World War I, assuming you overcame all of the situational obstacles and achieved surprise. You might even win two or three battles, as most enemy conventional weapons would be useless against the tank, and very vulnerable to them. But sooner or later, you'd run out of supplies, break down, or your enemy would wise up and not fight you in battle at all, choosing intrigue of many sorts until they removed the threat or its crew.
Before the 1800's, even a brilliant historian/linguist tank crew will have a lot of problems even making friends with their desired allies, as you'll be trusted perhaps less than we would trust space aliens with flying saucers saying they are here to help us atomize our enemies. Less, because of the fantastic context shift - for example if they are Christian, they'll probably think you are devils sent from Satan. Anyone who allies with you may be considered to have made a pact with the devil, be excommunicated, etc. Any powermongers you ally with are liable to scheme against you, and if they don't, some of their friends or enemies will. They'll feed you drugged food and it'll be interrogation time, or worse.