Number two in chinese: 二 vs 两
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.