How to estimate a histogram for two correlated input parameters when the resulting histogram is known?

• Let's assume there are two (slightly correlated) parameters (A and B).
• Both parameters are rated with discrete values (range: 1-5).
• The sum of the two parameter-ratings gives the cumulative-rating (A+B, range: 2-10).

How can I estimate the distribution (histogram) of the rating A and B, given that I know (or require):

• the distribution of the cumulative-rating (e.g. 0.10%, 0.30%, 3.20%, 12.00%, 51.20%, 22.00%, 9.70%, 1.50%)
• the correlation of A-rating and B-rating (e.g. 0.3)

Preferably I would like to use python to find the distribution. It seems to me, that I would need to find the solution iteratively but I don't know which approach would be used here.