In 1911 E. Teis learnt drawing and painting in water colours at a Sunday School in Saratov. In 1913, he studied at the Bogolybov's College of Graphic Artists. When the family moved to Tiflis (Tbilisi) E. Teis attended the O.I. Shlefling's Art School. At the same time he was engaged as a scene-painter at The Tiflis Opera House under A. A. Zaltsman's directorship. During 1921 - 1929 E. Teis studied at the Graphics Department of the Vhutemas under the tutelage of such masters as V.A. Favorsky, I.I. Nivinsky, N.N. Kupreyanov, P.Ya. Pavlinov and N.I. Piskarev.

Since 1923 he has been taught by P.V. Miturich, whose creative personality left a great impact upon his artistic vision. In 1924 E. Teis took part in mounting of Lenin's Mausoleum following the working drafts by Nivinsky. Between 1934 - 1939 he was engaged as a designer at the Polytechnical  Museum and the at  All-Union Agricultural Exhibition. Since 1934 E. Teis followed teaching as a career: he taught etching and drawing at the Extension Courses' Institute under the City Committee of Graphics Artists and in the State Museum of Fine Arts. E. Teis was an instructor in "The VseKoKhudozhnik"(The All-Union Cooperative Association) (1938).

In 1944-47 he taught at the Moscow Architectural Institute. In 1952-56 he was a teacher of drawing at the Moscow Higher College of Applied Arts (former Stroganov's College). In 1934 he devoted himself to creative and experimental fields at the Studio named after I.I. Nivinsky. By the year 1955 and up to 1967 E. Teis acquired the headship of the same Studio. Between 1940s - 60s more than once he obtained the author's certificates for elaborating of new methods of printing.