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It seems that there is very little information about E.B.E around.
There is a short Japanese article on www.advintage.jp
http://journal.advintage.jp/?eid=247
Google translation:
https://translate.google.com/translate?hl=de&sl=ja&tl=en&u=http://journal.advintage.jp/?eid=247
got this old Longines watch from late 1940s in a special case.
If so, a little bit of searching reveals that Edward Browing Eustance held several patents from 1930 through 1950, one of which was for the adjustable lugs: