His artistic beginnings are linked to the Castell dels Tres Dragons workshop (Parc de la Ciutadella, currently the home of the Natural Science Museum) and La Llotja, the Barcelona School of Fine Arts, while he was learning the trade of a typesetter.

He completed his studies thanks to a travel grant from the Barcelona Provincial Council which enabled him to go to Florence, Brussels, Paris and Rome, where he was influenced by the French and Italian Academicists. In this period he already presented a work at the 1891 Barcelona Fine Arts Exhibition, which enabled him to get himself known, although at this time his pieces bear witness to an attachment to narrative subject matters. Shortly afterwards, in 1896, he joined the Cercle Artístic de Sant Lluc (Artistic Circle of Saint Luke). A work from this period is Bust de matrona representant Barcelona (Bust of a Matron Representing Barcelona, 1897; MNAC collection).

His best known and most outstanding artistic production is decorative sculpture applied to architecture, with a lot of female figures with sweet faces and dresses that merge into the background where the figures are set.

He worked regularly with the architect J. Puig i Cadafalch, producing sculptures for Casa Amatller (1898-1900; Passeig de Gràcia, 41), Casa Macaya (1899-1901; Passeig de Sant Joan, 108) and Casa Trinxet (1902-1904; Còrsega, 268; no longer in existence); with L. Domènech i Montaner, making the fireplace in Fonda Espanya in 1901 (1903; Sant Pau, 9-11), the sculpture on the façade of Casa Lleó Morera (1905; Passeig de Gràcia, 35), and sculptural work for the Palau de la Música Catalana (1905-1908; Palau de la Música, 4-6) and the Hospital de la Santa Creu i Sant Pau (1902-1930; Sant Antoni Maria Claret, 167); and also with A. Falguera and P. Falqués, doing the sculpture on Casa de la Lactància (Nursing Mothers' Home, 1908-1913; Gran Via de les Corts Catalanes, 475-477), among others.

E. Arnau was also highly regarded as an expert medal maker - he was commissioned with making a large number of the official medals of the period - and as a goldsmith, working regularly with L. Masriera.