Are you familiar with computer engineering?
No but my daughter is a software engineer.
That's awesome.  Computer engineers integrate several fields of electrical engineering and computer science.  They develop computer hardware and software (like your daughter).
Please tell me the differences between system engineering and software engineering.
Computer engineers are involved in the hardware and software of computing (microprocessors, PC's, supercomputers, and circuit design). 
Which one is harder?
study in their junior and senior year because the full breadth of knowledge used in the design and application of computers is beyond the scope of an undergraduate degree. Other institutions may require engineering students to complete one or two years of general engineering before declaring computer engineering as their primary focus.
History.
Computer engineering began in 1939 when John Vincent Atanasoff and Clifford Berry began developing the world's first electronic digital computer through physics, mathematics, and electrical engineering. John Vincent Atanasoff was once a physics and mathematics teacher for Iowa
Outline of computer engineering
The following outline is provided as an overview of and topical guide to computer engineering:
Computer engineering – discipline that integrates several fields of electrical engineering and computer science required to develop computer hardware and software. Computer engineers usually have training in electronic engineering (or electrical engineering), software design, and hardware-software integration instead of only software engineering or electronic engineering. Computer engineers are involved in many hardware and software aspects of computing, from the design of individual microcontrollers, microprocessors, personal computers,