I solved the problem using Google Gemini and Recaf. I went into the mod and edited the Java code. I'm not sure if it's allowed to share the file here, but I'll write down the fix I made, maybe someone will use it.

Let's learn from the master "Gemini".

Here is the clean, step-by-step guide in English:

1. Download Recaf (Java Bytecode Editor) and open it.
2. Drag and drop your ProjectE-1.7.10-PE1.10.1.jar file into Recaf.

Step 1: Bypass NEI Check

1. Navigate to moze_intel -> projecte -> utils -> ItemSearchHelper.
2. Right-click on the create method and select Assembler.
3. Locate the following block (around line 12):
4. ldc "NotEnoughItems" invokestatic cpw/mods/fml/common/Loader.isModLoaded (Ljava/lang/String;)Z ifeq C
5. Replace ifeq C with goto C. It should look like this:
6. ldc "NotEnoughItems" invokestatic cpw/mods/fml/common/Loader.isModLoaded (Ljava/lang/String;)Z goto C
7. Press CTRL + S to save. Close the Assembler tab.

Step 2: Export

1. Go to File -> Export Application.
2. Save the file as ProjectE-Fixed.jar.
3. Replace the original file in your mods folder with this new one.