Will it be difficult to pursue an engineering degree when I haven't taken classes in high school that pertain to engineering?

The first question I have back to you is if you have a passion to pursue engineering is there a reason you didn't take any classes in college in that area? Were they not offered? Also what type of engineering are you talking about, that could have an impact on my answer.

If you have only taken and passed the core classes in high school this should not stop you from pursuing a civil engineer degree program. You might have to take some extra math classes, but the college/ university will help you there Go for it and good luck.

I don't believe you need to have engineering classes taken already when you are in High School to pursue an Engineering career. If you have the drive to become a Civil Engineer, and that's what you like to do, go for it. But sit down with one of either your school counselor or a professional/college admission officer to get a plan together so you know what you are getting into. You may need to take some pre-requisite classes, but you can take them in community colleges with less cost to fulfill the requirement, and get you up to speed on the knowledge and skillsets.

As you can hear or read the business news, lots of companies are looking for engineers. Employment opportunity is looking good at present for Engineers.

Difficulty is relative. It is very dependent on you. For example, physics come to me easy; I got straight As in my physics courses while some struggled. On the other hand, I don't claim the same results when it comes to calculus because it did not come to me as easy. All in all, you don't need engineering courses to do well in engineering. You will take them there! However, you are going to need a good base in math, physics, and english.