Does 2 Peter 1:10 teach salvation can be gained through faith plus works? Therefore, brethren, be all the more diligent to make certain about His calling and choosing you; for as long as you practice these things, you ( 2 Peter 1:10 NASB)
2 Peter 1:10 teaches to make our calling and election sure not make our salvation sure.

calling is not our work- 2 Timothy 1:9

election is not our work-Romans 9:11

Therefore, if calling and election are both not our works then HOW are we to MAKE sure of it?

The answer is found in the Greek word " spoudasate" ( go fast by applying fully one's self with diligence) in the qualities said in v. 5-7.

Peter exhorts and reminds us redeemed persons to be diligent in those qualities because:

1.it is ours( v. 8a),

2.we have it (v. 8b) and 

3.we are practicing it( note the present continuous tense of poiountes in v. 10).

By exemplifying those qualities we are making 'sure' not making ourself 'save', that is, that we are indeed called and chosen by God apart from our works.

Just like James 2:26 and Philippians 2:12, we must show forth our faith by our works. Faith alone in Christ saves but works proves real faith.