How do I write this in proper notation? I was wondering if anyone could help with the below. I don't usually write maths so I'm not even sure what I'm trying to search for. 
I want to write the below as a single equation because in reality C and J are quite large terms. 
$V_1=C+J_2$ and $V_2=C+J_1$
Something like: 
For $i=1,2$
$V_i = C+J_{(\text{the other variable})}$
Thanks,
Kat
 A: I have a problem with your question. I strongly feel you are asking a wrong question.
When we write (mathematics or anything) one thing to keep in mind is whether we are able to communicate clearly and quickly.
Something that occupies less space in print is most likely takes extra time on the part of the reader to unravel. Here one extra equation is a matter of typing 4 or 5 letters.
It is not worth the trouble to pack two equations into one.
Someone said at the end of a long letter "Sorry for writing a long letter, I don't have the time to write a short one"!
The answers given to your question (accepted one and other) are at best amusing and not at all easy on the eyes, and puts extra burden on the reader. Writing them as two equations looks best. Look at the comments to the answer seeking clarifications, that should make my point clear.
A: One way:
$$V_i = C + J_{3-i}, \quad i=1,2$$
Another:
$$\mathbf{V} = \sigma \mathbf{J} + \mathbf{C}, \quad\text{where}
\,\mathbf{V} = \left(\begin{matrix}V_1 \\ V_2\end{matrix}\right),
\,\mathbf{J} = \left(\begin{matrix}J_1 \\ J_2\end{matrix}\right),
\,\sigma = \left(\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right),
\,\mathbf{C} = \left(\begin{matrix}C \\ C\end{matrix}\right)
$$
A: $$V_i=C+J_{i\%2+1} \quad \forall \quad i=1,2$$ if this is what you're asking for.
