How to find a passenger manifest who left New York City to Europe around 1885-1913? I know he arrived to New York City, and there are 4 records at Ellis Island of people who would match him almost perfectly, but I know he returned home after maybe a year in New York City.
As @ColeValleyGirl says, this is rather a broad question and it would be easier to give a more specific answer with more knowledge of what country they might have been going to.
As far as I know there are no passenger lists for passengers leaving the US which means you will need to look for records of people arriving in Europe.
I believe that it wasn't uncommon for passengers to continental europe to travel via the UK so it's possible you might find them in the UK lists anyway, though only if they actually changed ship rather than if their ship just called in the UK en route.
The only passenger lists currently on-line for people leaving the U.S. are those for entry in the UK (as discussed in TomH's answer) and entry to Canada (not all crossing points). There may be archived copies in the various countries with international ports, but I have more than 15 such ports referenced in my database for relatives leaving Austria-Hungary.
In addition to bracketing the return date with other records (census, marriage, birth and death), sometimes a later return to the U.S. will generate additional evidence. These include the previous U.S. residence column on post-1905 passenger lists (although error-prone), and passport applications (both for naturalized citizens leaving on a trip, and for American-born children taken to Europe wanting to return).
A search at the US National Archives' catalog for the keywords 'passenger lists departing' will find several catalog entries for passenger lists, many from Record Group 85.
Ancestry has digitized several of these collections, as part of their database U.S., Departing Passenger and Crew Lists, 1914-1965 (dbid=60882), which was added on 14 January 2016.
The about the database article contains a 'View Sources' link to another page which lists the included records with their National Archives catalog identifier (NAI).
The records closest in time to your target date range are:
Registers of Vessels Departing from New York, New York, 8/11/1917 - 12/31/1971. NARA microform publication A3487. NAI: 3730419. Records of the Immigration and Naturalization Service, 1787–2004, Record Group 85. The National Archives at Washington, D.C.
However, it isn't clear how the user can choose to view the records from 1917. Choosing "New York" in the browse box doesn't show any records from A3487.
General information about the records at NARA can be found in their online Guide to Federal Records. The introduction to RG 85 is on the page Records of the Immigration and Naturalization Service [INS].