Hello
There is no direct way to achieve what you want rigth now. But since you are a developer you will be able to modify the files as required with reasonable amount of work. By that I mean that I have made a great effort keeping the code documented and as clean as possible.
So, first of all E!A is based in CodeIgniter v2 so you will have to read the documentation before messing with any files. You will also need to check the current file structure so that you can easily find the files you seek.
First modify the ea_users table of the database and add the fields you need. Then modify the /application/controllers/appointments.php controller as needed. You will also need to display the data in booking form so modify the /application/views/appointments.php. Finally update the frontend_book.js so that your data are collected from the booking form as done with the rest of the fields.
The backend page works in a similar way. Unfortunately there is no quick way to do this without getting your hands dirty :P
Best Regards,
Alex