Can WD Element work on Mac and PC at the same time?

I have WD Element 2TB and I used to connect with my PC and already had a lot of information in it. Recently I bought a macbook pro and I want to use the same external drive too. I can view the files in the external drive but I can’t edit / add / delete anything. 

Is it possible to use it on both platform without formatting my Elements?

Many thanks!

Yes

you can format on the Mac as MS-DOS ( FAT32 )

or you can use NTFS-3G