Robotics can be currently broken down in three main components: mechanics, electronics and then ... comes the fuzzy part, that is where there was used to be just computer science while in the recent past we see that many contributions are capitalized by people of diverse expertises, ranging from machine learning to even psychology (because robotics is getting a technology that can be enjoyed by a broader audience).
An electronic engineer is usually required to design the embedded boards that control the robot actuation, gather data from the sensors and exchange such information over the bus connecting the distributed system. His duty is thus mostly to deal with the hardware design of the boards so as the coding of the firmware, which is the special software (often written in C/C++) running on the boards that performs the activities outlined above on a regular basis (scheduling). This is the classical scenario.
Nonetheless, as an electronic engineer normally gets graduated with a solid background also in those disciplines that stand at higher level with respect to the world of physical boards (i.e. system identification, control theory, signal processing ...), he can apply his knowledge and develop it further (perhaps with a master and/or PhD) to problems and topics such as motor coordination, autonomous learning, grasping, vision processing, navigation, that all belong somehow to that third fuzzy area. In this zone of the "mind", being able to code software is somehow mandatory, whereas for the bodyware of the robot, you can focus just on the electronic design and neglect the firmware.