Cardinality of the set {10, (8+2)} Is |{10, (8+2)}| = 2?  (cardinality of the set)
I'm not sure about this because 8+2 = 10.  I know the cardinality of the set {10, 10} = 1, but since 8+2 is a different representation of 10, it could be different?  Any one can enlighten me on this?
Thanks!

You are a bit right, and a bit wrong. 
The set contains two distinct terms. However from the axioms of PA/rings/fields (or whatever axioms you work with) we can prove the terms are equal, and the set is equal to the singleton.
So as terms, the set has two elements. But if one works within a theory (as one usually does) then the set has provably but one element.
