You can find concrete information about colleges and higher education institutions in the website of the Japan Student Services Organization ( JASSO).
http://www.jasso.go.jp/study_j/schinfo_e.html#UThe site is available in English as well.
Almost all universities offer programmes in Engineering other than specialized universities that offer limited number of courses in very specific areas such as animation. However, your choice of University will depend on your preferred major, preferred location and of course your language capabilities. Please note that there are many universities that offer engineering programmes in English. Specially in Kanto area.
You can use the following search engine of JASSO to look for a uni that offers your desired programme. The site is unfortunately in Japanese. Please use google chrome with translation option on.
http://www.g-studyinjapan.jasso.go.jp/univ_search/Hope this helps.