After making a transaction and receiving all the hashes and ids, is there a number that is secret and only the two people involved in the transaction know?
Yes. You can view a transaction as being a public link between a number of public keys. If different people have the secret keys for those public keys then they have all the necessary information to calculate shared Diffie-Helman elliptic curve points. So in the simple case that you transfer all the bitcoins in an address to someone else's address then you can use his address and your private key to calculate a point which will be the same as the point calculated by him using his private key and your address. Nobody else can calculate these points.