Maltosyltransferase that uses maltose 1-phosphate (M1P) as the sugar donor to elongate linear or branched alpha-(1->4)-glucans. Is also able to catalyze the reverse reaction in vitro. Cannot use glucose 1-phosphate as substrate. Is involved in a branched alpha-glucan biosynthetic pathway from trehalose, together with TreS, Mak and GlgB. [(1->4)-alpha-D-glucosyl](n) + alpha-maltose 1-phosphate = [(1->4)-alpha-D-glucosyl](n+2) + phosphate The transfer reaction from maltose-1-P to glycogen is inhibited by micromolar amounts of inorganic phosphate or arsenate but is only slightly inhibited by millimolar concentrations of glucose-1-P, glucose-6-P, or inorganic pyrophosphate. Is also inhibited by ATP, by 1,4-dideoxy-1,4-imino-D-arabinitol (DIA), but not by isofagomine. The data are not very reliable because measures were done with a partially purified enzyme. Glycan biosynthesis; glycogen biosynthesis. Homodimer. Cells lacking this gene display M1P accumulation and trehalose sensitivity. These phenotypes are suppressed in mutants lacking both glgE and treS or both glgE and mak. Deletion of glgE does not increase glycogen content. Belongs to the glycosyl hydrolase 13 family. GlgE subfamily. Truncated N-terminus.