2016 income $10,000 investment loss -$100,000
2015 income $10,000 investment gain $75,000
Can I apply loss from 2016 to gain in 2015?
If yes, how?
The short answer is no, an individual may not carryback capital losses. 26 USC 1212
(b) Other taxpayers
Your question implies this is investment income and losses. Therefore the above answer would stand.
If you are in the trade or business of being a broker, trader in securities, or in the trade or business of dealing in securities for your own account, the answer would be different. It would qualify as a business loss, giving rise to a net operating loss that could be carried back.
It is a high hurdle to claim trade or business for your own account. The IRS does provide guidance. Note that if you claim it for losses, you also have to claim it for gains, thus subject to ordinary earnings and self-employment tax.