Rather than saying that 两 is used with nouns, I would say that 两 is used with measure words. If you use any type of measure word with the number 2, use 两. For convenience, I've identified 3 types of measure words:
Standard measure words, e.g. 两个人、两本书、两棵树.
Numbers that are larger than 100, e.g. 两百, 两千三百六十二. 百, 千, and 万 can be seen as a sort of measure word.
Time, e.g. 下午两点. Again, 点 functions as a type of measure word here.
二 is used when counting without measure words, such as in telephone numbers, metro lines (二线), addresses, etc.
- ordinal, e.g. 第二个, 二哥. when you want to say the second, you can only use 二, it is wrong to say that 第两个.