Convert exponential to normal distribution
You can use sklearn.preprocessing.QuantileTransformer (or sklearn.preprocessing.PowerTransformer) which does exactly what you want:

from sklearn.preprocessing import QuantileTransformer
import numpy as np

ey = np.random.exponential(size=100)
qt = QuantileTransformer(output_distribution='normal')
no = qt.fit_transform(ey.reshape(-1, 1))


You can plot histograms to compare "before" vs "after":

# Plot histograms to see before vs after.
import matplotlib.pyplot as plt
%matplotlib inline 
plt.subplot(2, 2, 1)
plt.hist(ey, bins='auto')
plt.subplot(2, 2, 2)
plt.hist(no, bins='auto')
plt.show()




The advantage of this approach is that it will also work for other input distributions, not only exponential.