I have two opposite answers to the question. The first is that the first partition won't affect the second, so go ahead. The second is "Is it worth the risk to you?"
If I were in your shoes, my feet would hurt because they are size 13. No, I mean that if I were in your shoes, I would do a complete disk backup to an external drive. With the right kind of backup (and be plenty sure that it is the right kind), if you destroy all of the partitions on the original drive you can restore the backup and go on your merry way with both OSes working again.
If you have a good backup and restore system, nothing can really ruin your system because you can always restore to a known point.
In the best case, the re-installation should leave the E partition functional, but it will not be in your boot menu since the Win10 installation will likely ignore it. You will either need to work with the BCDEDIT tool or install a separate boot manager. This _might_ not happen if you install Win10 directly over the C partition while said partition can still be booted - but won't work if you format the partition before doing the install.
Anyone out there have more recent experience with Win10 boot management than I do?