I have just received a job offer from my potential employer.

However, there is something that worries me. I have a 2nd income, from my position as a director of a subsidiary of my current company, and I did not disclose it in my resume and during the job interview. The reason I didn't disclose the info is to honour confidentiality and due strategic business reasons.

I have no intention to mislead the potential employer, but I'm afraid they will question my honesty if they found out about it after doing a background check on me. I definitely don't want to jeopardize this job opportunity.

Anyhow, I'm going to resign from both positions.

So how can I disclose this 2nd job to my potential employer in my job acceptance reply, while maintaining professionalism?

Is there any particular reason why you feel the need to tell your new employer any of this?