Reddit mentions of Tensors, Differential Forms, and Variational Principles (Dover Books on Mathematics)

Read this for the basic algebriac perspective (really only need the super short first chapter on tensors), then this for the application to general relativity, which is, to a good approximation, just tensor analysis on manifolds (mainly chapter 2 and 3).

As SDogwood said you need an intro in proofs. Unfortunately I know of no better way to do this than to sit in on a class such as "intro to abstract algebra", I took it as a junior level course. I can't even tell you what book to use, cause the prof wrote their own ~100 page book and sold it as notes for like $5. The most difficult part of the class was actually having the will power to show up. I did almost no work outside of the class. One of the things that the department required the class do is make the students present a proof, normally 3 students at the beginning of class and you would rotate through the roster. Shockingly it was one of the more fun classes I took. If you can do this it is probably your best option. I know engineering curriculums can be tight, but you really should see if maybe there is a night version or something, its worth it.

I would also suggest just picking out some dover books like this one and working through it on your own. Stuff like that you won't need proofs for and depending on what type of engineer you are may also be of help.

Although it has already been answered, I recommend the book "Tensors, Differential Forms and Variational Principles" by Lovelock and Rund. From what I gather, you are looking for a more analytic approach and this is exactly what that book offers. It's a Dover publication, hence it is very cheap (currently under $10).
Link to its American amazon page

I have been trying to study tensor calculus in my own time. I have this and this book. I'm finding it a bit difficult. Any suggestions?