They have not left you with a gap.
Financial aid is based on the following premise COA- EFC = Demonstrated need.
They determined your EFC to b e 13K
Amherst met your demonstrated need.
Unfortunately, it is going to be a struggle to pay your EFC (not an unusual occurrence). If there are no loans in your financial aid package, you can use your loans to pay your EFC. However, it is highly unlikely than Amherst is going to take your EFC from 13K to 0 to cover housing.