@Andy Lu , You should always have a very clear agreement prior to the purchase. I am a strong believer that to make any partnership work it has to be equal beneficial to all parties involved.
Each partner should receive back what they put into the property. Then the net should be divided between both partners. Rent payments covered mortgage so you would have to take in consideration any +/- moneys after monthly payments.
If you managed the property for 10 years, normally there should be a 6% management fee per month. This would equal to around $14,400 over the duration of the partnership. It would be unfair because you are actually managing your own property that you have a 50% ownership. So you may want to minimize the percentage to 3%.
Based on your numbers. Your all in cost was $300K the resale is $360K this leaves $28,800 net after the closing cost.
The problem with such a long term partnership without legal documents outlining the conditions, contributions and exit financials becomes a issue. Especially when it's business between friends. Over the years if one partner is doing more or feels they've put in a higher stake in the venture then stress or division can occur in the partnership. Unfortunately this develops into a right of entitlement over the other. Of course I do not know your position nor do I state that this is your scenario just some information for others whom may read this post.