The easiest way to do a not so easy math problem in your head is to approach it as more than one easy math problem. With reciprical headings, you really want to add or subtract 180 degrees. It is easier to add or subtract 200 degrees (340 - 200 = 140) but we know that isn't correct because we added or subtracted 20 too much so we correct it by subtracting or adding back 20 degrees (140 + 20 = 160) which is the recip heading for 340. Because of going beyound 0/360 degrees sometimes you have to add 200 and subtract 20, other times you have to subtract 200 and add 20. That is exactly what the add 2 to one number and subtract 2 from the other (or vice versa) is doing. Of course, if you are in a plane, the quickest and easiest is simply to look at you DG or OBS. Recipricals are always on opposite sides of the dial. Find the number that you want the recip of and then look straight across the dial for its recip.
There is a similar approach to converting Celcius to Fahrenheit in your head. Most people can't do 9/5s in their head but they can double a number. Doubling a number and then subtracting 1/10 of the result is the same as 9/5 so take 15 deg. C, double it (30), subtract 1/10 (30-3=27). now you still have to add the 27 to 32 to get degrees F. If that is too difficult, then add it to 30 and then add 2 more. (=59F)