The difficulty settings actually affect the game on a LOT of different levels so the ramp up between them is pretty tough:
Easy:
1. Base global panic starts at 0
2. Most alien activity only raises panic by 1 in left unchecked
3. Your soldiers have 1 bonus hitpoint
4. Aliens are dumber, and there aren't as many of them
5. Soldiers cost $10
Normal:
1. Base global panic starts at 0
2. Most minor alien activity raises panic by 1 in left unchecked with some events doing up to 3
3. Your soldiers have no bonus hitpoints
4. Aliens have their AI mostly unshackled
5. Soldiers cost $10
Classic:
1. Base global panic starts at 8 (1 per location)
2. If unchecked alien activity causes at least 1 panic, but will often cause 2 or 3
3. Your soldiers have -1 hitpoint
4. All aliens receive bonuses hit hitpoints, accuracy, critical change and / or damage.
5. Alien AI is unshackled
6. You receive no officer training school
7. There are even more aliens per map
8. Soldiers cost $15
Impossible:
1. Base global panic starts at 16 (2 per location)
2. If unchecked alien activity causes at least 2 panic, but will often cause even more
3. Your soldiers have -2 hitpoints
4. All aliens receive bonuses hit hitpoints, accuracy, critical change and / or damage.
5. Alien AI is unshackled
6. You receive no officer training school
7. There are even more aliens per map
8. Soldiers cost $15
So playing on Impossible it is very likely you will lose one or more funding nation on month one. In theory you could lose every funding nation of the first month depending on alien activity and the efficacy of your response so good luck commander.