Question 1209008
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For the original number we have
t = tens digit
u = units digit
That constructs 10t+u


For instance if the number is 23 then t = 2 and u = 3.
10t+u = 10*2+3 = 23.


The digits of Sophie's mystery number add to 6.
t+u = 6 which solves to <font color=blue>u = 6-t</font>
This will be useful in a substitution later.


10u+t is the result of reversing the digits. This is 45 less than her favorite number.


swapped = original - 45
10u + t = 10t+u - 45
10(<font color=blue>u</font>) + t = 10t+<font color=blue>u</font> - 45
10(<font color=blue>6-t</font>) + t = 10t+<font color=blue>6-t</font> - 45
60-10t+t = 10t+6-t-45
60-9t = 9t-39
-9t-9t = -39-60
-18t = -99
t = -99/(-18)
t = 5.5
We do not get a whole number result for the tens digit, so there must be a typo somewhere in your question. 
Perhaps the digits add to something else other than 6? 
Or maybe the "45" should be another value?
I would ask your teacher for clarification.
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