so is there a smarter way to permanently store the mobile numbers once entered?
Smarter than what? Using 10 bytes in EEPROM to store a 10 digit phone number is not going to break the bank.
If not, what is the best way to use EEPROM
There are two main functions - read() and write(). Each puts or gets one byte/char from one address in EEPROM. Dirt simple to use, really.