Being a long time user of the E1 boards myself, I would say that you MAY be able to do this. As I don't have the specs handy right now, I can suggest a means by which to come up with the solution for yourself:
Check the specs of the board. You are looking for the specs for the DAQ STC timer portion, as you want to do counting operations, not data acquisition. I don't remember if the DAQ STC on the E1 can handle 10MHz. If it doesn't, stop there, and get your NI Catalog and look for one of the newer boards with the advanced timing chips, I believe these can handle it. If the E1 can handle it, go on from there. Create a timing diagram for yourself, to get a visual picture of what you need. Then determine what gating and triggering you need. There are numerous
examples in the sample programs database in LabVIEW for counting. These should point you in the right direction.
Good luck