Hey there!! 
First, Let’s take the number as ‘ x ‘ 
Given : the bigger number is 18 more than twice the smaller number. 
Small number - x 
Bigger number - 2x + 18 
Their sum = 93 
Equation : 
x + 2x + 18 = 93 
3x + 18 = 93 
Subtract 18 on both sides 
3x = 75 
Divide 3 on both sides 
x = 25 
Hence , small number is 25 
Small number + big number = 93 
25 + big number = 93 
Big number = 93 - 35 
Big number = 68 
Hope my answer helps!!