Geldman was born at a displaced persons camp in Munich to Polish parents who had survived the Holocaust. His family immigrated to Israel in 1949 and settled in Tel Aviv, where he has lived ever since. He completed a bachelor's in literature and a master's in clinical psychology at Bar Ilan University.
Geldman spent six years in residency as a psychotherapist. He later established a unit for the selection of managers at Pilat management services and served as a clinical psychologist at the IDF center for the evaluation of senior officers. He is currently an independent psychotherapist using psychoanalytical methods.
Geldman's poetry is philosophical, psychological, and existentialistic. It combines literary Hebrew and everyday language, even some slang. He published 11 poetry books and 6 non-fiction books.
As a visual artist Geldman is engaged in plastic arts, ceramics and photography. His photographs were exhibited at such places as the Tel Aviv Museum of Art. Geldman was an art critic of the Israeli daily Haaretz, and treasured exhibitions for many Israeli artists.