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:

 1. *Standard measure words*, e.g. 两个人、两本书、两棵树.

 2. *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. 

 3. *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. 

 4. *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.