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?