% of unknown number when trying to find unknown number

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I'm working on a spreadsheet for my small real estate business and I'm stuck on a math problem.

I want to find the minimum rent I can charge for a property to still break even. I know the monthly mortgage and all my expenses except 2: vacancy coverage and management fees. These 2 numbers are 5% and 10% of the rent, respectively. The issue is that I'm trying to figure out the rent, but 2 of the numbers I need are contingent on the rent. Here's what I think is right, but it doesn't make sense:

Rent = mortgage + expenses + (15% of rent)

But how do I find the 15% of the rent when that 15% is part of the number?

(I am not looking at profit for this exercise...just my break even point, so my goal is for this to end up being total expenses - rent = 0.)

Thanks in advance.

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$$ R = M + E + 0.15R $$ so $$ (1-0.15)R = M+E $$ so $$ R = \frac{M+E}{0.85}. $$