Hello Ramakant,

EE namely Electronics Engineering. This branch basically deals with pure Electronics. You will be taught about circuit theory, Electronic instruments, Digital and Analog Electronics, vlsi and lot more in more depth as compared to ECE. 
This field is purely electronics nothing more in the core except that. Only in the first year you will have some subjects from other branches which will be common between all branches.

ECE namely Electronics and Communication or Electronics and Telecommunication Engineering is something more related to Communication rather than Electronics. As I mentioned, The first year subjects will be from all branches and common between all. 
From second year you will get some basics of Electronics, most of the times its the overview part not very deep, however from third year you will be dealing with only Telecommunications till the end. You will study RF and Microwave Engineering, mobile, Satellite Communications, analog and digital communication, RADAR, Computer Networks, Internet etc.

Hope it helps you

Thank you