The key to pick out the Hikari is getting the complete daily timetable between the two cities. Just search the normal way. It will give you the Nozomi as a default. Click on the clock on the timetable button to the right of the Nozomi train and it will give you every Shinkansen of every flavor for the whole day between Kyoto and Tokyo Stations. In your case you could take the Hakari at 10AM which gets in Tokyo at 12:43 PM. The next NEX leaves Tokyo at 1:03 PM followed by the 1:33 PM one. It's a little work using the Hyperdia timetable, but it's a fantastic tool.