10 years
1) Considering that we can call the age of a stamp by "s" and the age of a coin by "c" we can write out the following system of Linear Equations:

Note that we can solve it using the Elimination Method.
2) So let's add simultaneously both equations:

We can plug into that s=10 and find the age of a coin as well:

Note that we subtracted 20 from both sides.
3) Hence, the age of a stamp is 10 years