by White Flame

To subtract A from a number, or “number - .A”, we transform it to the doable “-.A + number”:

 eor #$ff
 sec
 adc number

and that's it.

by Frantic

One may think that the following two pieces of code would produce exactly the same result:

  ;Variant 1 - Subtract XX by YY using clc/adc
  lda #XX
  clc
  adc #YY  ;E.g. to subtract with 1, use $ff here

  ;Variant 2 - Subtract $XX by $YY using sec/adc
  lda #XX
  sec
  adc #YY-1  ;E.g. to subtract with 1, use $ff-1=$fe here

The resulting byte in the A register will indeed be the same for all possible values (0-255) of value XX and YY in each of the two variants. However, the carry flag will be set differently after executing these two pieces of code for various values of XX and YY.

This means that if the value of the carry after the “subtraction” matters to you, you can't use standard addition form (clc/adc) to do the “subtraction”. White Flame's code above is obviously using the correct version of inverse subtraction (e.g. sec/adc).