In long addition the overflow is carried across columns like so
$$ \begin{array}{cccc} & \tiny{1} & \tiny{1} & \\ & 3 & 5 & 8 \\ + & 2 & 9 & 6 \\ \hline \\ & 6 & 5 & 4 \\ \end{array} $$
I'm doing some crypto work at the moment and I need to perform an operation like long addition except the carries are disregarded:
$$ \require{cancel} \begin{array}{cccc} & \cancel{\tiny{1}} & \cancel{\tiny{1}} & \\ & 3 & 5 & 8 \\ + & 2 & 9 & 6 \\ \hline \\ & 5 & 4 & 4 \\ \end{array} $$
Is there a way to do this in a fixed number of steps? If the addends were in binary, I could do this in one step with a simple bitwise XOR. But in decimal, I'm finding I have to do it digit by digit, which is time consuming. I've been doodling around with things like 10's complement but I can't think of anything.
Also does this operation have a name? "Digitwise addition" doesn't seem to be a thing. It's a struggle to Google this because the keywords are so generic.
P.S. I'm also interested in long subtraction that disregards the borrows. :-)