You can schedule the transaction using a scheduling service:
However, as you need the other party to be able to see the transaction need to create a contract, put the ether there (so the other party can see that you are doing your part) and require the scheduling service to execute a transaction in your contract that sends the ether to the other party in ten days. This is actually easier than it sounds.
Also if you do not need this to be automatic, you can skip the scheduling service and just add a conditional in your contract so that the other party can take the ether in a particular date and not before.
Disclaimer: I wrote the ChronosAion service.
Hope this helps