In terms of reputation, one way to minimise the difference between the two answers is to upvote and accept the answer (by ticking it) you think is the most clear and of higher quality. This would gain them +25 rep. For the other answer, you can upvote too and provide the bounty of +50. This would gain them +60 rep; the difference is only 35 rep.
As @Mars had pointed out below, the difference in reputation can slowly be reduced as the accepted answer floats to the top and naturally, more people would upvote that one.
As has been said in the comments, you need to wait two days to start a bounty. After that time, a link for 'start a bounty' will appear under 'add a comment', in which you can select the amount (+50), and the reason, which you can choose Reward existing answer - One or more of the answers is exemplary and is worthy of an additional bounty.
Note that at any one time, at most three bounties can be started by one person. From your profile I see you've already started one, so as long as you don't start two more before this question you'll be fine.
N.B. In some cases, when you don't award the bounty of +50 within seven days and the grace period, only a bounty of +25 is given to the other answerer. This way may work as well. For further details, see here, taken from the Help Centre:
If you do not award your bounty within 7 days (plus the grace period), the highest voted answer created after the bounty started with a minimum score of 2 will be awarded half the bounty amount (or the full amount, if the answer is also accepted). If two or more eligible answers have the same score (their scores are tied), the oldest answer is chosen. If there's no answer meeting those criteria, no bounty is awarded to anyone.
If the bounty was started by the question owner, and the question owner accepts an answer posted during the bounty period, and the bounty expires without an explicit award then we assume the bounty owner liked the answer they accepted and award it the full bounty amount at the time of bounty expiration.