Brain blocked on recalling this formula

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The discussion centers on developing a mixing fluid calculator to determine the masses of two components (m1 and m2) based on known temperatures and total volume. The user has successfully solved for the final temperature (Tf) but seeks a method to calculate both m1 and m2 when the total mass (mt) is known. Given a total volume of 99ml at 20 degrees Celsius, with initial temperatures T1 at 25 degrees and T2 at 10 degrees, the user proposes a formula for m2: m2 = m1 (T1 - Tf) / (Tf - T2). The conversation emphasizes the need for a simultaneous calculation of m1 and m2 within a spreadsheet framework, highlighting the challenge of achieving this with the provided data.
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TL;DR
Need to manipulate T(final) = (m1_T1 + m2_T2) / (m1 + m2) to solve for m2
Trying to build a mixing fluid calculator and cannot for the life of me figure out how to solve for m2 rather then Tf

Got an answer to question 1, but bonus question: is there anyway to solve for m2 and m1 if mt is known?

IE given a total volume of mixture IE 99ml, at 20 deg. I know T1 is 25 deg, and T2 is 10.. Using the math it tells me I need 33ml of T2 and 66ml of T1. This will be built into a spreadsheet, is there anyway to calculate both t1 and t2 at the same time?
 
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I suggest it is,
m2 = m1 (T1 - Tf) / (Tf - T2)
 
tech99 said:
I suggest it is,
m2 = m1 (T1 - Tf) / (Tf - T2)
Thank you so much!
 

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