Step 1: Find original data for company E from the table:
Total employees = 4240
Female employees = 2600
Step 2: The female employees increased by 10%, so the new number of female employees is:
\[
2600 + 10% \times 2600 = 2600 + 260 = 2860
\]
Step 3: Since total employees remain the same at 4240, the number of male employees now is:
\[
\text{Male employees} = \text{Total employees} - \text{New female employees} = 4240 - 2860 = 1380
\]
Therefore, the number of male employees after the increase is \(\boxed{1380}\).