abbreviation of "house".
you can read this word "hse" mostly in classified ads since most advertisers wanna minimize on their expense by maximizing use of spaces in a three line ad. Mostly and commonly used as
"open hse".
HSE Uncle Curtis: (to anyone who will listen, at a rapid tempo) "I tell you what, everyday I come home from work, I have a ham sandwich uh-hum, uh-hum.''