Apply partial styling to text in excel cell using EPpplus

You should try to use ExcelRichText class. For example:

var newFile = new FileInfo("example.xlsx");
using (var package = new ExcelPackage(newFile))
{
    var worksheet = package.Workbook.Worksheets.Add("Example");

    var boldRichText = worksheet.Cells[1, 1].RichText.Add("Hello");
    boldRichText.Bold = true;

    var normalRichText = worksheet.Cells[1, 1].RichText.Add(" World");
    normalRichText.Bold = false;

    package.Save();
}