normal distribution and z scores

[maxpower2]

im trying to find the mean and standard deviation for player A finishing positions in a tournament.

we know 15% he finishes in the top 10.
we know 10% he finishes in the bottom 20

https://www.youtube.com/watch?v=t727GFJB-ZU

i was watching above for how to do this on paper. there is a slight difference in what im using this method for. so if any maths guys could let me know if this is the wrong method for the problem.

i can make the formulas p(z<a)=15%
and p(z<b)=90%

i use the =norm.s.inv(0.15) to solve and get z scores of -1.03643 and 1.281552

now on paper we have 2 equations -1.03=10-mean/standard div and 1.28=20-mean/sd and we can solve them

but how do i use excel to solve this to get the mean and sd for the player. any guidance on how do do this greatly appreciated. my maths is v rusty and any better methods (or correct ones if im wrong) would be great to hear too. im hoping i will be able to get probabilities for say top 30% from this once i have the mean and sd or am i mistaken? thanks in advance