I own a house and I'm thinking of taking a job in another city. I would need to rent an Apartment to stay at. Can I deduct rent and expenses? Im not self employed.

No.   Your rent and living expenses would be personal expenses,  not deductible on a tax return.   And moving expenses are not deductible on a federal return except for certain members of the military.

--W-2 employees cannot deduct job-related expenses on a federal return.  Job-related expenses were eliminated as a federal deduction for W-2 employees by the tax laws that changed for 2018 and beyond.  Your state tax laws might be different in AL, AR, CA, HI, MN, NY or PA.

If you live in a state that lets you deduct job-related expenses, the information will flow from your federal return  to the state return, so enter it in Federal>Deductions and Credits>Employment Expenses>Job-Related Expenses

https://ttlc.intuit.com/questions/4482873-which-federal-tax-deductions-have-been-suspended-by-tax-reform

Per the tax laws that changed for 2018 and beyond, moving expenses are not deductible on a federal return except for certain active duty members of the military.

There are several states that allow a deduction for moving expenses on the state return:  AZ, AR, CA, HI, IA, MA, MN, NJ, NY, PA and VA  You can enter your moving expenses in the federal software and the information will flow to your state return.