Edward Thuftin emigrating under his brother's name is a bit of a mystery, but it can be considered proven that this is what happened. Here's the evidence at hand:

Christening and confirmation records have Edward born November 17th 1882 and Torvald born August 28th 1888.

The emigration record in Oslo is for Thorvald Torstens. Langbraaten from S. Aurdal, 16 years of age at departure September 30th 1904, which is a perfect fit for Torvald, but on arrival as Torvald Torsteinsen his age is given as 18. (Assuming this is the correct record.)

Torvald appears as sponsor in the christening records of neighbours' children in 1905, 1906 and 1907, on the 1910 Norwegian census with the correct birth date, as born 1889 at his wedding in 1911, but the correct 1888 at the christenings of his first two children.

Edward on the other hand is recorded on his WWI registration from 1917 as born November 20th 1887, as 32 years of age in the 1920 US census and 42 in the 1930 census.

The three day difference for Edward's birthday is easily explained as either an error when the date was told to the minister or the family misremembering it later. This leaves us with the only discrepancies being the name on the emigration record and Edward's birth year in the US. The conclusion then follows that Edward, for unknown reasons, used his brother's papers to leave Norway, and didn't mind being six years younger once he got his own name back. 

Citations

  1. [S328] Arland Independent Cemetery, http://www.rootsweb.ancestry.com/~wibarron/cemeteries/…, Thuftin, Edward, born 20 Nov 1886, died 28 May 1949, marked Father WWI 163 Dept Brid WI Pvt.
  2. [S6] Folketelling 1900, Torstein Knudsen - Langbraaten, Sør-Aurdal, Oppland.
  3. [S2] Living relative, Ed's son, Donald Thuftin.
  4. [S345] USC 1930, Household of Ed Thuftun/Thufteen, sheet 4A, Arland Township, Barron, Wisconsin.
  5. [S296] Sør-Aurdal 1877-1885, folio 110, døbte 1882, no. 96, født 17/11, døbt 25/12, Edvard, Bgd. (Begndalen), foreldre Hmd. Torstein Knudsen 1855(sic), Gunhild Maria Hansdtr 1852(sic) Langbraaten (Sørum).
  6. [S306] Begnadalen 1894-1921, folio 49, Konfirmationsdag d. 7de juni 1897, no. 3 Edvart Torstensen, født 17.11.82, døbt 25.12.82.
  7. [S17] Emigration 1867-1930 Oslo, Thorvald Torstens. Langbraaten emigration 30.9.1904.
  8. [S342] Canada to US border crossings, Torvald Torsteinsen arriving at Quebec.