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To me, Computer Engineering would encompass the lower-level aspects of computing, such as the manufacture of electronics from silicon, the hardware or microprocessor architecture, microcontrollers up to the low-level bits and logic of the operating system. You will typically see Computer Engineers fiddling with circuit boards and oscilloscopes and soldering irons and stuff.
On the other hand, Software Engineering would be dealing much more on the software or high-level side of building software, such as designing a framework for a web application, developing a game on the scale of World of Warcraft, developing Google Chrome/Chromium, building an operating system; they work with all kinds of large-scale and complex software projects.
You have folks who are called Computer Engineers who actually do Software Engineering though, but otherwise Computer Engineering is sort-of a sub-discipline of Electrical Engineering focused on building computing machines.
In addition to Electrical Engineering, Computer Engineering includes Networking, which cuts across issues of Software and lower-level issues.
Also remember that a solution sometimes requires more than Software -- you might need a whole server farm, or some specialized hardware. Someone other than a Software engineer typically looks at quality issues such as robustness, responsiveness, and reliability.