Salwe was born into a Jewish family in Warsaw. He was Szlama Zalman's son. He gained the knowledge about chess very early but started playing chess only at about 20 years old. In 1894, he settled in Łódź at Nowocegielniana Street 10. In 1897, Salwe took 2nd at the 1st Łódź Chess Championship. In 1898, he won a Łódź championship. In 1903, he took 4th at Kiev. Salwe reached a peak of his career in 1906, when he won at Sankt Petersburg, ahead of Benjamin Blumenfeld and Akiba Rubinstein. In 1906, he took 4th at Łódź. In 1906, he took 3rd at Łódź. In 1906, he tied for 6-7th at Nuremberg. In 1906, he played in famous 2nd tournament at Ostend, where he took 3rd, 2nd, 2nd-3rd, 4th, and tied for 5-6th. The event was won by Carl Schlechter. In 1907, he took 4th at Łódź. In 1907, he took 8th at Ostend. In 1907, he took 9th at Carlsbad. In 1907/08, he tied for 3rd-4th with Eugene Znosko-Borovsky, behind Rubinstein and Simon Alapin, at Łódź. In 1908, he took 13th at Vienna. In 1908, he tied for 7-9th at Prague. In 1908, he took 2nd, behind Marshall, at Düsseldorf. In 1908, he took 3rd, behind Rubinstein and Marshall, at Łódź. In 1908, he took 2nd, behind Alapin, at Warsaw. In 1909, he tied for 8-10th at Sankt Petersburg. The event was won by Emanuel Lasker and Rubinstein. In 1909, he took 5th at Vilna. The event was won by Rubinstein. In 1910, he tied for 11-14th at Hamburg. In 1911, he tied for 17-18th at Carlsbad. In 1911, he tied for 2nd-3rd with Alexander Flamberg, behind Rubinstein, at Warsaw. In 1912, he took 3rd at Warsaw. In 1912, he tied for 9-11th at Bad Pistyan. In 1912, he took 10th at Vilna. In 1912, he took 3rd, behind Efim Bogoljubow and Flamberg, at Łódź. In 1913, he won at Łódź. In 1914, he won at Łódź. In 1913/14, he tied for 10-11th at Sankt Petersburg. During World War I, he took 2nd in 1915, won in 1916, and took 2nd, behind Rubinstein, in 1917 at Łódź. Salwe played several matches in Łódź. In 1903, he drew a match against Rubinstein. In 1904, he lost to Rubinstein. In 1904, he drew with Chigorin. In 1905, he won a match against Jacques Mieses. In 1906, he lost a match against Chigorin. In 1908, he lost to Rubinstein. In 1909, he won a match against Gersz Rotlewi. In 1910, he lost to Rotlewi. In 1913, he lost to Oldřich Duras. In 1913, he lost to Bogoljubow. Salwe was the chief editor of the chess newspaper in Yiddish "Erste Yidishe Shahtsaytung" First Jewish Chess Newspaper". The [first issue was released in October 1913. The 1st World War caused to closing it. Salwe was buried in the Jewish Cemetery in Łódź at Bracka Street.
