First, I suggest that you run an EFA with correlated factors, using an oblique rotation. This is because your two factors may be highly correlated, which would point toward combining them.

Also, if you do want to calculate coefficient alpha, you will need to un-reverse the two items, since it assumes that all the correlations are positive.

It is frequently the case that positively and negatively worded items load onto different factors. The reason is that the correlations within each set of items (positive vs. negative) tend to be higher than across sets. If you enter a keyword string such as "positive negative item effects" into Google Scholar, you can find a number of methodological articles that deal with this issue.

Several pubs on reverse scoring (e.g., Woods, C. M. (2006) ‘Careless responding to reverse-worded items: Implications for confirmatory factory analysis’, Journal of Psychopathology and Behavioral Assessment, 28(3), 189-194. Available at: https://doi.org/10.1007/s10862-005-9004-7). The biggest issue comes when people just add negations to otherwise positive statements. This increases RTs and lowers reliability (e.g., Article Measuring Empathizing and Systemizing with a Large US Sample